diff --git a/Library/Homebrew/formula_cellar_checks.rb b/Library/Homebrew/formula_cellar_checks.rb
index 77e6050314..cff0baa647 100644
--- a/Library/Homebrew/formula_cellar_checks.rb
+++ b/Library/Homebrew/formula_cellar_checks.rb
@@ -314,6 +314,24 @@ module FormulaCellarChecks
     "No `cpuid` instruction detected. #{formula} should not use `ENV.runtime_cpu_detection`."
   end
 
+  def check_binary_arches(formula)
+    return unless formula.prefix.directory?
+    # There is no `binary_executable_or_library_files` method for the generic OS
+    return if !OS.mac? && !OS.linux?
+
+    keg = Keg.new(formula.prefix)
+    mismatches = keg.binary_executable_or_library_files.reject do |file|
+      file.arch == Hardware::CPU.arch
+    end
+    return if mismatches.empty?
+
+    <<~EOS
+      Binaries built for a non-native architecture were installed into #{formula}'s prefix.
+      The offending files are:
+        #{mismatches * "\n        "}
+    EOS
+  end
+
   def audit_installed
     @new_formula ||= false
 
@@ -334,6 +352,7 @@ module FormulaCellarChecks
     problem_if_output(check_plist(formula.prefix, formula.plist))
     problem_if_output(check_python_symlinks(formula.name, formula.keg_only?))
     problem_if_output(check_cpuid_instruction(formula))
+    problem_if_output(check_binary_arches(formula))
   end
   alias generic_audit_installed audit_installed
 
diff --git a/Library/Homebrew/os/linux/elf.rb b/Library/Homebrew/os/linux/elf.rb
index f31a40f806..77bf6f4139 100644
--- a/Library/Homebrew/os/linux/elf.rb
+++ b/Library/Homebrew/os/linux/elf.rb
@@ -33,7 +33,7 @@ module ELFShim
   private_constant :ARCHITECTURE_POWERPC
   ARCHITECTURE_ARM = 0x28
   private_constant :ARCHITECTURE_ARM
-  ARCHITECTURE_X86_64 = 0x62
+  ARCHITECTURE_X86_64 = 0x3E
   private_constant :ARCHITECTURE_X86_64
   ARCHITECTURE_AARCH64 = 0xB7
   private_constant :ARCHITECTURE_AARCH64
diff --git a/Library/Homebrew/os/mac/mach.rb b/Library/Homebrew/os/mac/mach.rb
index adae8e32f6..0b4d8a0c63 100644
--- a/Library/Homebrew/os/mac/mach.rb
+++ b/Library/Homebrew/os/mac/mach.rb
@@ -29,7 +29,7 @@ module MachOShim
 
       machos.each do |m|
         arch = case m.cputype
-        when :x86_64, :i386, :ppc64 then m.cputype
+        when :x86_64, :i386, :ppc64, :arm64, :arm then m.cputype
         when :ppc then :ppc7400
         else :dunno
         end