diff --git a/changelog/fix_performance_issue_for_multiline_element_indentation.md b/changelog/fix_performance_issue_for_multiline_element_indentation.md
new file mode 100644
index 00000000000..1aa7f7972df
--- /dev/null
+++ b/changelog/fix_performance_issue_for_multiline_element_indentation.md
@@ -0,0 +1 @@
+* [#10764](https://github.com/rubocop/rubocop/issues/10764): Fix performance issue for Layout/FirstHashElementIndentation and Layout/FirstArrayElementIndentation. ([@j-miyake][])
diff --git a/lib/rubocop/cop/layout/first_array_element_indentation.rb b/lib/rubocop/cop/layout/first_array_element_indentation.rb
index e857df41ffc..e138f02b7b5 100644
--- a/lib/rubocop/cop/layout/first_array_element_indentation.rb
+++ b/lib/rubocop/cop/layout/first_array_element_indentation.rb
@@ -120,14 +120,15 @@ def check(array_node, left_parenthesis)
             check_first(first_elem, left_bracket, left_parenthesis, 0)
           end
 
-          check_right_bracket(array_node.loc.end, left_bracket, left_parenthesis)
+          check_right_bracket(array_node.loc.end, first_elem, left_bracket, left_parenthesis)
         end
 
-        def check_right_bracket(right_bracket, left_bracket, left_parenthesis)
+        def check_right_bracket(right_bracket, first_elem, left_bracket, left_parenthesis)
           # if the right bracket is on the same line as the last value, accept
           return if /\S/.match?(right_bracket.source_line[0...right_bracket.column])
 
-          expected_column, indent_base_type = indent_base(left_bracket, left_parenthesis)
+          expected_column, indent_base_type = indent_base(left_bracket, first_elem,
+                                                          left_parenthesis)
           @column_delta = expected_column - right_bracket.column
           return if @column_delta.zero?
 
diff --git a/lib/rubocop/cop/layout/first_hash_element_indentation.rb b/lib/rubocop/cop/layout/first_hash_element_indentation.rb
index 625aab71175..d0e85136437 100644
--- a/lib/rubocop/cop/layout/first_hash_element_indentation.rb
+++ b/lib/rubocop/cop/layout/first_hash_element_indentation.rb
@@ -158,14 +158,14 @@ def check(hash_node, left_parenthesis)
             end
           end
 
-          check_right_brace(hash_node.loc.end, left_brace, left_parenthesis)
+          check_right_brace(hash_node.loc.end, first_pair, left_brace, left_parenthesis)
         end
 
-        def check_right_brace(right_brace, left_brace, left_parenthesis)
+        def check_right_brace(right_brace, first_pair, left_brace, left_parenthesis)
           # if the right brace is on the same line as the last value, accept
           return if /\S/.match?(right_brace.source_line[0...right_brace.column])
 
-          expected_column, indent_base_type = indent_base(left_brace, left_parenthesis)
+          expected_column, indent_base_type = indent_base(left_brace, first_pair, left_parenthesis)
           @column_delta = expected_column - right_brace.column
           return if @column_delta.zero?
 
diff --git a/lib/rubocop/cop/mixin/multiline_element_indentation.rb b/lib/rubocop/cop/mixin/multiline_element_indentation.rb
index f90f5cde6cc..b49005b459e 100644
--- a/lib/rubocop/cop/mixin/multiline_element_indentation.rb
+++ b/lib/rubocop/cop/mixin/multiline_element_indentation.rb
@@ -26,7 +26,7 @@ def each_argument_node(node, type)
       def check_first(first, left_brace, left_parenthesis, offset)
         actual_column = first.source_range.column
 
-        indent_base_column, indent_base_type = indent_base(left_brace, left_parenthesis)
+        indent_base_column, indent_base_type = indent_base(left_brace, first, left_parenthesis)
         expected_column = indent_base_column + configured_indentation_width + offset
 
         @column_delta = expected_column - actual_column
@@ -47,10 +47,10 @@ def check_expected_style(styles)
         end
       end
 
-      def indent_base(left_brace, left_parenthesis)
+      def indent_base(left_brace, first, left_parenthesis)
         return [left_brace.column, :left_brace_or_bracket] if style == brace_alignment_style
 
-        pair = hash_pair_where_value_beginning_with(left_brace)
+        pair = hash_pair_where_value_beginning_with(left_brace, first)
         if pair && key_and_value_begin_on_same_line?(pair) &&
            right_sibling_begins_on_subsequent_line?(pair)
           return [pair.loc.column, :parent_hash_key]
@@ -63,17 +63,10 @@ def indent_base(left_brace, left_parenthesis)
         [left_brace.source_line =~ /\S/, :start_of_line]
       end
 
-      def hash_pair_where_value_beginning_with(left_brace)
-        node = node_beginning_with(left_brace)
-        node.parent&.pair_type? ? node.parent : nil
-      end
+      def hash_pair_where_value_beginning_with(left_brace, first)
+        return unless first && first.parent.loc.begin == left_brace
 
-      def node_beginning_with(left_brace)
-        processed_source.ast.each_descendant do |node|
-          if node.loc.is_a?(Parser::Source::Map::Collection) && (node.loc.begin == left_brace)
-            break node
-          end
-        end
+        first.parent&.parent&.pair_type? ? first.parent.parent : nil
       end
 
       def key_and_value_begin_on_same_line?(pair)