diff --git a/Library/Homebrew/rubocops/lines.rb b/Library/Homebrew/rubocops/lines.rb
index 3e9f8a9cc5a6f..31f84d57b9040 100644
--- a/Library/Homebrew/rubocops/lines.rb
+++ b/Library/Homebrew/rubocops/lines.rb
@@ -157,6 +157,24 @@ def unless_modifier?(node)
         end
       end
 
+      class MpiCheck < FormulaCop
+        def audit_formula(_node, _class_node, _parent_class_node, body_node)
+          # Enforce use of OpenMPI for MPI dependency in core
+          return unless formula_tap == "homebrew-core"
+
+          find_method_with_args(body_node, :depends_on, "mpich") do
+            problem "Use 'depends_on \"open-mpi\"' instead of '#{@offensive_node.source}'."
+          end
+        end
+
+        def autocorrect(node)
+          # The dependency nodes may need to be re-sorted because of this
+          lambda do |corrector|
+            corrector.replace(node.source_range, "depends_on \"open-mpi\"")
+          end
+        end
+      end
+
       class Miscellaneous < FormulaCop
         def audit_formula(_node, _class_node, _parent_class_node, body_node)
           # FileUtils is included in Formula
diff --git a/Library/Homebrew/rubocops/text.rb b/Library/Homebrew/rubocops/text.rb
index e328e63585d47..ec8130abb7e2a 100644
--- a/Library/Homebrew/rubocops/text.rb
+++ b/Library/Homebrew/rubocops/text.rb
@@ -16,7 +16,7 @@ def audit_formula(_node, _class_node, _parent_class_node, body_node)
             problem "Formulae should not depend on both OpenSSL and LibreSSL (even optionally)."
           end
 
-          if depends_on?("veclibfort") || depends_on?("lapack")
+          if formula_tap == "homebrew-core" && (depends_on?("veclibfort") || depends_on?("lapack"))
             problem "Formulae should use OpenBLAS as the default serial linear algebra library."
           end
 
diff --git a/Library/Homebrew/test/rubocops/lines_spec.rb b/Library/Homebrew/test/rubocops/lines_spec.rb
index 2ad2497185559..7f11573288ff0 100644
--- a/Library/Homebrew/test/rubocops/lines_spec.rb
+++ b/Library/Homebrew/test/rubocops/lines_spec.rb
@@ -279,6 +279,31 @@ def options
   end
 end
 
+describe RuboCop::Cop::FormulaAudit::MpiCheck do
+  subject(:cop) { described_class.new }
+
+  context "When auditing formula" do
+    it "reports an offense when using depends_on \"mpich\"" do
+      expect_offense(<<~RUBY, "/homebrew-core/")
+        class Foo < Formula
+          desc "foo"
+          url 'https://brew.sh/foo-1.0.tgz'
+          depends_on "mpich"
+          ^^^^^^^^^^^^^^^^^^ Use 'depends_on "open-mpi"' instead of 'depends_on "mpich"'.
+        end
+      RUBY
+
+      expect_correction(<<~RUBY)
+        class Foo < Formula
+          desc "foo"
+          url 'https://brew.sh/foo-1.0.tgz'
+          depends_on "open-mpi"
+        end
+      RUBY
+    end
+  end
+end
+
 describe RuboCop::Cop::FormulaAudit::Miscellaneous do
   subject(:cop) { described_class.new }
 
diff --git a/Library/Homebrew/test/rubocops/text_spec.rb b/Library/Homebrew/test/rubocops/text_spec.rb
index 8485c5c4fec1c..f185fcbc9a8a1 100644
--- a/Library/Homebrew/test/rubocops/text_spec.rb
+++ b/Library/Homebrew/test/rubocops/text_spec.rb
@@ -32,6 +32,28 @@ class Foo < Formula
       RUBY
     end
 
+    it "when veclibfort is used instead of OpenBLAS" do
+      expect_offense(<<~RUBY, "/homebrew-core/")
+        class Foo < Formula
+          url "https://brew.sh/foo-1.0.tgz"
+          homepage "https://brew.sh"
+          depends_on "veclibfort"
+          ^^^^^^^^^^^^^^^^^^^^^^^ Formulae should use OpenBLAS as the default serial linear algebra library.
+        end
+      RUBY
+    end
+
+    it "when lapack is used instead of OpenBLAS" do
+      expect_offense(<<~RUBY, "/homebrew-core/")
+        class Foo < Formula
+          url "https://brew.sh/foo-1.0.tgz"
+          homepage "https://brew.sh"
+          depends_on "lapack"
+          ^^^^^^^^^^^^^^^^^^^ Formulae should use OpenBLAS as the default serial linear algebra library.
+        end
+      RUBY
+    end
+
     it "When xcodebuild is called without SYMROOT" do
       expect_offense(<<~RUBY)
         class Foo < Formula