diff --git a/dbms/src/Storages/AlterCommands.cpp b/dbms/src/Storages/AlterCommands.cpp
index 3c75f806ad1..6748f56a5ab 100644
--- a/dbms/src/Storages/AlterCommands.cpp
+++ b/dbms/src/Storages/AlterCommands.cpp
@@ -477,4 +477,15 @@ void AlterCommands::validate(const IStorage & table, const Context & context)
     }
 }
 
+bool AlterCommands::is_mutable() const
+{
+    for (const auto & param : *this)
+    {
+        if (param.is_mutable())
+            return true;
+    }
+
+    return false;
+}
+
 }
diff --git a/dbms/src/Storages/AlterCommands.h b/dbms/src/Storages/AlterCommands.h
index ac6d74d249a..e870e2f9762 100644
--- a/dbms/src/Storages/AlterCommands.h
+++ b/dbms/src/Storages/AlterCommands.h
@@ -70,6 +70,7 @@ public:
     void apply(ColumnsDescription & columns_description) const;
 
     void validate(const IStorage & table, const Context & context);
+    bool is_mutable() const;
 };
 
 }
diff --git a/dbms/src/Storages/MergeTree/MergeTreeData.cpp b/dbms/src/Storages/MergeTree/MergeTreeData.cpp
index 012991db465..a9126dc79a9 100644
--- a/dbms/src/Storages/MergeTree/MergeTreeData.cpp
+++ b/dbms/src/Storages/MergeTree/MergeTreeData.cpp
@@ -908,7 +908,7 @@ void MergeTreeData::checkAlter(const AlterCommands & commands)
 
     for (const AlterCommand & command : commands)
     {
-        if (command.type == AlterCommand::COMMENT_COLUMN)
+        if (!command.is_mutable())
         {
             continue;
         }
diff --git a/dbms/src/Storages/StorageMergeTree.cpp b/dbms/src/Storages/StorageMergeTree.cpp
index 0e926218a05..2686427fa74 100644
--- a/dbms/src/Storages/StorageMergeTree.cpp
+++ b/dbms/src/Storages/StorageMergeTree.cpp
@@ -188,6 +188,16 @@ void StorageMergeTree::alter(
     const String & table_name,
     const Context & context)
 {
+    if (!params.is_mutable())
+    {
+        auto table_soft_lock = lockStructureForAlter(__PRETTY_FUNCTION__);
+        auto new_columns = getColumns();
+        params.apply(new_columns);
+        context.getDatabase(database_name)->alterTable(context, table_name, new_columns, {});
+        setColumns(std::move(new_columns));
+        return;
+    }
+
     /// NOTE: Here, as in ReplicatedMergeTree, you can do ALTER which does not block the writing of data for a long time.
     auto merge_blocker = merger_mutator.actions_blocker.cancel();
 
diff --git a/dbms/tests/queries/0_stateless/00725_comment_columns.reference b/dbms/tests/queries/0_stateless/00725_comment_columns.reference
index 19dac99b721..ca4edfb3122 100644
--- a/dbms/tests/queries/0_stateless/00725_comment_columns.reference
+++ b/dbms/tests/queries/0_stateless/00725_comment_columns.reference
@@ -1,28 +1,38 @@
-CREATE TABLE test.check_query_comment_column ( first_column UInt8 DEFAULT 1 COMMENT \'first comment\',  fourth_column UInt8 COMMENT \'fourth comment\',  fifth_column UInt8,  second_column UInt8 MATERIALIZED first_column COMMENT \'second comment\',  third_column UInt8 ALIAS second_column COMMENT \'third comment\') ENGINE = TinyLog
-┌─table──────────────────────┬─name──────────┬─comment────────┐
-│ check_query_comment_column │ first_column  │ first comment  │
-│ check_query_comment_column │ fourth_column │ fourth comment │
-│ check_query_comment_column │ fifth_column  │                │
-│ check_query_comment_column │ second_column │ second comment │
-│ check_query_comment_column │ third_column  │ third comment  │
-└────────────────────────────┴───────────────┴────────────────┘
-CREATE TABLE test.check_query_comment_column ( first_column UInt8 DEFAULT 1 COMMENT \'another first column\',  fourth_column UInt8 COMMENT \'another fourth column\',  fifth_column UInt8 COMMENT \'another fifth column\',  second_column UInt8 MATERIALIZED first_column COMMENT \'another second column\',  third_column UInt8 ALIAS second_column COMMENT \'another third column\') ENGINE = TinyLog
-┌─table──────────────────────┬─name──────────┬─comment───────────────┐
-│ check_query_comment_column │ first_column  │ another first column  │
-│ check_query_comment_column │ fourth_column │ another fourth column │
-│ check_query_comment_column │ fifth_column  │ another fifth column  │
-│ check_query_comment_column │ second_column │ another second column │
-│ check_query_comment_column │ third_column  │ another third column  │
-└────────────────────────────┴───────────────┴───────────────────────┘
-CREATE TABLE test.check_query_comment_column ( first_column Date COMMENT \'first comment\',  second_column UInt8 COMMENT \'second comment\',  third_column UInt8 COMMENT \'third comment\') ENGINE = MergeTree(first_column, (second_column, second_column), 8192)
-┌─table──────────────────────┬─name──────────┬─comment────────┐
-│ check_query_comment_column │ first_column  │ first comment  │
-│ check_query_comment_column │ second_column │ second comment │
-│ check_query_comment_column │ third_column  │ third comment  │
-└────────────────────────────┴───────────────┴────────────────┘
-CREATE TABLE test.check_query_comment_column ( first_column Date COMMENT \'another first comment\',  second_column UInt8 COMMENT \'another second comment\',  third_column UInt8 COMMENT \'another third comment\') ENGINE = MergeTree(first_column, (second_column, second_column), 8192)
-┌─table──────────────────────┬─name──────────┬─comment────────────────┐
-│ check_query_comment_column │ first_column  │ another first comment  │
-│ check_query_comment_column │ second_column │ another second comment │
-│ check_query_comment_column │ third_column  │ another third comment  │
-└────────────────────────────┴───────────────┴────────────────────────┘
+CREATE TABLE test.check_query_comment_column ( first_column UInt8 DEFAULT 1 COMMENT \'comment 1\',  fourth_column UInt8 COMMENT \'comment 4\',  fifth_column UInt8,  second_column UInt8 MATERIALIZED first_column COMMENT \'comment 2\',  third_column UInt8 ALIAS second_column COMMENT \'comment 3\') ENGINE = TinyLog
+first_column	UInt8	DEFAULT	1	comment 1
+fourth_column	UInt8			comment 4
+fifth_column	UInt8			
+second_column	UInt8	MATERIALIZED	first_column	comment 2
+third_column	UInt8	ALIAS	second_column	comment 3
+┌─table──────────────────────┬─name──────────┬─comment───┐
+│ check_query_comment_column │ first_column  │ comment 1 │
+│ check_query_comment_column │ fourth_column │ comment 4 │
+│ check_query_comment_column │ fifth_column  │           │
+│ check_query_comment_column │ second_column │ comment 2 │
+│ check_query_comment_column │ third_column  │ comment 3 │
+└────────────────────────────┴───────────────┴───────────┘
+CREATE TABLE test.check_query_comment_column ( first_column UInt8 DEFAULT 1 COMMENT \'comment 1_1\',  fourth_column UInt8 COMMENT \'comment 4_1\',  fifth_column UInt8 COMMENT \'comment 5_1\',  second_column UInt8 MATERIALIZED first_column COMMENT \'comment 2_1\',  third_column UInt8 ALIAS second_column COMMENT \'comment 3_1\') ENGINE = TinyLog
+┌─table──────────────────────┬─name──────────┬─comment─────┐
+│ check_query_comment_column │ first_column  │ comment 1_2 │
+│ check_query_comment_column │ fourth_column │ comment 4_2 │
+│ check_query_comment_column │ fifth_column  │ comment 5_2 │
+│ check_query_comment_column │ second_column │ comment 2_2 │
+│ check_query_comment_column │ third_column  │ comment 3_2 │
+└────────────────────────────┴───────────────┴─────────────┘
+CREATE TABLE test.check_query_comment_column ( first_column UInt8 DEFAULT 1 COMMENT \'comment 1_2\',  fourth_column UInt8 COMMENT \'comment 4_2\',  fifth_column UInt8 COMMENT \'comment 5_2\',  second_column UInt8 MATERIALIZED first_column COMMENT \'comment 2_2\',  third_column UInt8 ALIAS second_column COMMENT \'comment 3_2\') ENGINE = TinyLog
+CREATE TABLE test.check_query_comment_column ( first_column UInt8 COMMENT \'comment 1\',  second_column UInt8 COMMENT \'comment 2\',  third_column UInt8 COMMENT \'comment 3\') ENGINE = MergeTree() PARTITION BY second_column ORDER BY first_column SAMPLE BY first_column SETTINGS index_granularity = 8192
+first_column	UInt8			comment 1
+second_column	UInt8			comment 2
+third_column	UInt8			comment 3
+┌─table──────────────────────┬─name──────────┬─comment───┐
+│ check_query_comment_column │ first_column  │ comment 1 │
+│ check_query_comment_column │ second_column │ comment 2 │
+│ check_query_comment_column │ third_column  │ comment 3 │
+└────────────────────────────┴───────────────┴───────────┘
+CREATE TABLE test.check_query_comment_column ( first_column UInt8 COMMENT \'comment 1_2\',  second_column UInt8 COMMENT \'comment 2_2\',  third_column UInt8 COMMENT \'comment 3_2\') ENGINE = MergeTree() PARTITION BY second_column ORDER BY first_column SAMPLE BY first_column SETTINGS index_granularity = 8192
+CREATE TABLE test.check_query_comment_column ( first_column UInt8 COMMENT \'comment 1_3\',  second_column UInt8 COMMENT \'comment 2_3\',  third_column UInt8 COMMENT \'comment 3_3\') ENGINE = MergeTree() PARTITION BY second_column ORDER BY first_column SAMPLE BY first_column SETTINGS index_granularity = 8192
+┌─table──────────────────────┬─name──────────┬─comment─────┐
+│ check_query_comment_column │ first_column  │ comment 1_3 │
+│ check_query_comment_column │ second_column │ comment 2_3 │
+│ check_query_comment_column │ third_column  │ comment 3_3 │
+└────────────────────────────┴───────────────┴─────────────┘
diff --git a/dbms/tests/queries/0_stateless/00725_comment_columns.sql b/dbms/tests/queries/0_stateless/00725_comment_columns.sql
index ada4e4e1983..97667616983 100644
--- a/dbms/tests/queries/0_stateless/00725_comment_columns.sql
+++ b/dbms/tests/queries/0_stateless/00725_comment_columns.sql
@@ -1,16 +1,18 @@
 CREATE DATABASE IF NOT EXISTS test;
 DROP TABLE IF EXISTS test.check_query_comment_column;
 
+-- Check COMMENT COLUMN and MODIFY COLUMN statements with simple engine
 CREATE TABLE test.check_query_comment_column
   (
-    first_column UInt8 DEFAULT 1 COMMENT 'first comment',
-    second_column UInt8 MATERIALIZED first_column COMMENT 'second comment',
-    third_column UInt8 ALIAS second_column COMMENT 'third comment',
-    fourth_column UInt8 COMMENT 'fourth comment',
+    first_column UInt8 DEFAULT 1 COMMENT 'comment 1',
+    second_column UInt8 MATERIALIZED first_column COMMENT 'comment 2',
+    third_column UInt8 ALIAS second_column COMMENT 'comment 3',
+    fourth_column UInt8 COMMENT 'comment 4',
     fifth_column UInt8
   ) ENGINE = TinyLog;
 
 SHOW CREATE TABLE test.check_query_comment_column;
+DESCRIBE TABLE test.check_query_comment_column;
 
 SELECT table, name, comment
 FROM system.columns
@@ -18,30 +20,42 @@ WHERE table = 'check_query_comment_column' AND database = 'test'
 FORMAT PrettyCompactNoEscapes;
 
 ALTER TABLE test.check_query_comment_column
-  COMMENT COLUMN first_column 'another first column',
-  COMMENT COLUMN second_column 'another second column',
-  COMMENT COLUMN third_column 'another third column',
-  COMMENT COLUMN fourth_column 'another fourth column',
-  COMMENT COLUMN fifth_column 'another fifth column';
+  COMMENT COLUMN first_column 'comment 1_1',
+  COMMENT COLUMN second_column 'comment 2_1',
+  COMMENT COLUMN third_column 'comment 3_1',
+  COMMENT COLUMN fourth_column 'comment 4_1',
+  COMMENT COLUMN fifth_column 'comment 5_1';
 
 SHOW CREATE TABLE test.check_query_comment_column;
 
+ALTER TABLE test.check_query_comment_column
+  MODIFY COLUMN first_column COMMENT 'comment 1_2',
+  MODIFY COLUMN second_column COMMENT 'comment 2_2',
+  MODIFY COLUMN third_column COMMENT 'comment 3_2',
+  MODIFY COLUMN fourth_column COMMENT 'comment 4_2',
+  MODIFY COLUMN fifth_column COMMENT 'comment 5_2';
+
 SELECT table, name, comment
 FROM system.columns
 WHERE table = 'check_query_comment_column' AND database = 'test'
 FORMAT PrettyCompactNoEscapes;
 
+SHOW CREATE TABLE test.check_query_comment_column;
 DROP TABLE IF EXISTS test.check_query_comment_column;
 
-
+-- Check `ALTER TABLE table_name COMMENT COLUMN 'comment'` statement with MergeTree engine
 CREATE TABLE test.check_query_comment_column
   (
-    first_column Date COMMENT 'first comment',
-    second_column UInt8 COMMENT 'second comment',
-    third_column UInt8 COMMENT 'third comment'
-  ) ENGINE = MergeTree(first_column, (second_column, second_column), 8192);
+    first_column UInt8 COMMENT 'comment 1',
+    second_column UInt8 COMMENT 'comment 2',
+    third_column UInt8 COMMENT 'comment 3'
+  ) ENGINE = MergeTree()
+        ORDER BY first_column
+        PARTITION BY second_column
+        SAMPLE BY first_column;
 
 SHOW CREATE TABLE test.check_query_comment_column;
+DESCRIBE TABLE test.check_query_comment_column;
 
 SELECT table, name, comment
 FROM system.columns
@@ -49,25 +63,23 @@ WHERE table = 'check_query_comment_column' AND database = 'test'
 FORMAT PrettyCompactNoEscapes;
 
 ALTER TABLE test.check_query_comment_column
-  COMMENT COLUMN first_column 'another first comment',
-  COMMENT COLUMN second_column 'another second comment',
-  COMMENT COLUMN third_column 'another third comment';
+  COMMENT COLUMN first_column 'comment 1_2',
+  COMMENT COLUMN second_column 'comment 2_2',
+  COMMENT COLUMN third_column 'comment 3_2';
 
 SHOW CREATE TABLE test.check_query_comment_column;
 
-SELECT table, name, comment
-FROM system.columns
-WHERE table = 'check_query_comment_column' and database = 'test'
-FORMAT PrettyCompactNoEscapes;
+ALTER TABLE test.check_query_comment_column
+  MODIFY COLUMN first_column COMMENT 'comment 1_3',
+  MODIFY COLUMN second_column COMMENT 'comment 2_3',
+  MODIFY COLUMN third_column COMMENT 'comment 3_3';
 
-DROP TABLE IF test.check_query_comment_column;
+SHOW CREATE TABLE test.check_query_comment_column;
 
-CREATE TABLE test.check_query_comment_column
-  (
-    first_column UInt8 COMMENT 'first comment'
-  ) ENGINE = TinyLog;
-
-ALTER TABLE test.check_query_comment_column MODIFY COLUMN first_column COMMENT 'another comment';
+ALTER TABLE test.check_query_comment_column
+  MODIFY COLUMN first_column DEFAULT 1 COMMENT 'comment 1_3',
+  MODIFY COLUMN second_column COMMENT 'comment 2_3',            -- We can't change default value of partition key.
+  MODIFY COLUMN third_column DEFAULT 1 COMMENT 'comment 3_3';
 
 SELECT table, name, comment
 FROM system.columns
@@ -75,3 +87,5 @@ WHERE table = 'check_query_comment_column' and database = 'test'
 FORMAT PrettyCompactNoEscapes;
 
 DROP TABLE IF EXISTS test.check_query_comment_column;
+
+-- TODO: add here tests with ReplicatedMergeTree