diff --git a/Library/Homebrew/cask/dsl.rb b/Library/Homebrew/cask/dsl.rb
index d4d06da622..ef2ba0483c 100644
--- a/Library/Homebrew/cask/dsl.rb
+++ b/Library/Homebrew/cask/dsl.rb
@@ -243,6 +243,24 @@ module Cask
       end
     end
 
+    # @api public
+    def arch(arm: nil, intel: nil)
+      should_return = arm.blank? && intel.blank?
+
+      set_unique_stanza(:arch, should_return) do
+        @on_system_blocks_exist = true
+
+        # If arm and intel are arrays and one isn't specified, default to an array that is the same size as the other
+        empty_value = Array.new(arm&.count || intel&.count) if arm.is_a?(Array) || intel.is_a?(Array)
+
+        if OnSystem.arch_condition_met? :arm
+          arm || empty_value
+        elsif OnSystem.arch_condition_met? :intel
+          intel || empty_value
+        end
+      end
+    end
+
     # `depends_on` uses a load method so that multiple stanzas can be merged.
     # @api public
     def depends_on(*args)
diff --git a/Library/Homebrew/livecheck.rb b/Library/Homebrew/livecheck.rb
index 66abd5142f..f02eef7e1e 100644
--- a/Library/Homebrew/livecheck.rb
+++ b/Library/Homebrew/livecheck.rb
@@ -143,7 +143,8 @@ class Livecheck
   end
 
   delegate version: :@package_or_resource
-  private :version
+  delegate arch: :@package_or_resource
+  private :version, :arch
 
   # Returns a `Hash` of all instance variable values.
   # @return [Hash]
diff --git a/Library/Homebrew/rubocops/cask/constants/stanza.rb b/Library/Homebrew/rubocops/cask/constants/stanza.rb
index 93a9b67d55..959beda606 100644
--- a/Library/Homebrew/rubocops/cask/constants/stanza.rb
+++ b/Library/Homebrew/rubocops/cask/constants/stanza.rb
@@ -6,7 +6,7 @@ module RuboCop
     # Constants available globally for use in all cask cops.
     module Constants
       STANZA_GROUPS = [
-        [:version, :sha256],
+        [:version, :sha256, :arch],
         [:language],
         [:url, :appcast, :name, :desc, :homepage],
         [:livecheck],
diff --git a/Library/Homebrew/test/cask/dsl_spec.rb b/Library/Homebrew/test/cask/dsl_spec.rb
index f8f3c0ecf7..5700c869b5 100644
--- a/Library/Homebrew/test/cask/dsl_spec.rb
+++ b/Library/Homebrew/test/cask/dsl_spec.rb
@@ -305,6 +305,62 @@ describe Cask::DSL, :cask do
     end
   end
 
+  describe "arch stanza" do
+    let(:token) { "invalid/invalid-two-arch" }
+
+    it "prevents defining multiple arches" do
+      expect { cask }.to raise_error(Cask::CaskInvalidError, /'arch' stanza may only appear once/)
+    end
+
+    context "when only one string value is passed for intel" do
+      let(:token) { "one-string-arch" }
+
+      context "when running on arm" do
+        before do
+          allow(Hardware::CPU).to receive(:type).and_return(:arm)
+        end
+
+        it "returns the value" do
+          expect(cask.url.to_s).to eq "file://#{TEST_FIXTURE_DIR}/cask/caffeine-arm.zip"
+        end
+      end
+
+      context "when running on intel" do
+        before do
+          allow(Hardware::CPU).to receive(:type).and_return(:intel)
+        end
+
+        it "defaults to `nil` for the other when no arrays are passed" do
+          expect(cask.url.to_s).to eq "file://#{TEST_FIXTURE_DIR}/cask/caffeine.zip"
+        end
+      end
+    end
+
+    context "when only one array arch value is passed for intel" do
+      let(:token) { "one-array-arch" }
+
+      context "when running on arm" do
+        before do
+          allow(Hardware::CPU).to receive(:type).and_return(:arm)
+        end
+
+        it "defaults to an array of the same size as the other when an array is passed" do
+          expect(cask.url.to_s).to eq "file://#{TEST_FIXTURE_DIR}/cask/caffeine.zip"
+        end
+      end
+
+      context "when running on intel" do
+        before do
+          allow(Hardware::CPU).to receive(:type).and_return(:intel)
+        end
+
+        it "returns the value" do
+          expect(cask.url.to_s).to eq "file://#{TEST_FIXTURE_DIR}/cask/intel-caffeine-x86_64.zip"
+        end
+      end
+    end
+  end
+
   describe "appcast stanza" do
     let(:token) { "with-appcast" }
 
diff --git a/Library/Homebrew/test/support/fixtures/cask/Casks/invalid/invalid-two-arch.rb b/Library/Homebrew/test/support/fixtures/cask/Casks/invalid/invalid-two-arch.rb
new file mode 100644
index 0000000000..15112831e6
--- /dev/null
+++ b/Library/Homebrew/test/support/fixtures/cask/Casks/invalid/invalid-two-arch.rb
@@ -0,0 +1,11 @@
+cask "invalid-two-arch" do
+  version "1.2.3"
+  sha256 "67cdb8a02803ef37fdbf7e0be205863172e41a561ca446cd84f0d7ab35a99d94"
+  arch arm: "arm", intel: "intel"
+  arch arm: "amd64", intel: "x86_64"
+
+  url "file://#{TEST_FIXTURE_DIR}/cask/caffeine.zip"
+  homepage "https://brew.sh/"
+
+  app "Caffeine.app"
+end
diff --git a/Library/Homebrew/test/support/fixtures/cask/Casks/multiple-versions.rb b/Library/Homebrew/test/support/fixtures/cask/Casks/multiple-versions.rb
index ad05491a2d..a98420ab5b 100644
--- a/Library/Homebrew/test/support/fixtures/cask/Casks/multiple-versions.rb
+++ b/Library/Homebrew/test/support/fixtures/cask/Casks/multiple-versions.rb
@@ -1,11 +1,7 @@
 cask "multiple-versions" do
-  arch = "arm"
   version "1.2.3"
   sha256 "67cdb8a02803ef37fdbf7e0be205863172e41a561ca446cd84f0d7ab35a99d94"
-
-  on_intel do
-    arch = "intel"
-  end
+  arch arm: "arm", intel: "intel"
 
   on_big_sur do
     version "1.2.0"
diff --git a/Library/Homebrew/test/support/fixtures/cask/Casks/one-array-arch.rb b/Library/Homebrew/test/support/fixtures/cask/Casks/one-array-arch.rb
new file mode 100644
index 0000000000..7151fd9fbe
--- /dev/null
+++ b/Library/Homebrew/test/support/fixtures/cask/Casks/one-array-arch.rb
@@ -0,0 +1,10 @@
+cask "one-array-arch" do
+  version "1.2.3"
+  sha256 "67cdb8a02803ef37fdbf7e0be205863172e41a561ca446cd84f0d7ab35a99d94"
+  arch intel: ["intel-", "-x86_64"]
+
+  url "file://#{TEST_FIXTURE_DIR}/cask/#{arch.first}caffeine#{arch.last}.zip"
+  homepage "https://brew.sh/"
+
+  app "Caffeine.app"
+end
diff --git a/Library/Homebrew/test/support/fixtures/cask/Casks/one-string-arch.rb b/Library/Homebrew/test/support/fixtures/cask/Casks/one-string-arch.rb
new file mode 100644
index 0000000000..b808cdb4f5
--- /dev/null
+++ b/Library/Homebrew/test/support/fixtures/cask/Casks/one-string-arch.rb
@@ -0,0 +1,10 @@
+cask "one-string-arch" do
+  version "1.2.3"
+  sha256 "67cdb8a02803ef37fdbf7e0be205863172e41a561ca446cd84f0d7ab35a99d94"
+  arch arm: "-arm"
+
+  url "file://#{TEST_FIXTURE_DIR}/cask/caffeine#{arch}.zip"
+  homepage "https://brew.sh/"
+
+  app "Caffeine.app"
+end