diff --git a/History.md b/History.md
index a4a82a146..beb540117 100644
--- a/History.md
+++ b/History.md
@@ -9,6 +9,9 @@ Compatibility notes
   [[GitHub #266]](https://github.com/ruby/openssl/pull/266)
 * Deprecate `OpenSSL::Config#add_value` and `#[]=` for future removal.
   [[GitHub #322]](https://github.com/ruby/openssl/pull/322)
+* Deprecate algorithmic constants for `OpenSSL::Cipher` and `OpenSSL::Digest` 
+  for future removal.
+  [[GitHub #366]](https://github.com/ruby/openssl/pull/366)
 
 
 Notable changes
diff --git a/lib/openssl/cipher.rb b/lib/openssl/cipher.rb
index 8ad8c35dd..ffbc9c872 100644
--- a/lib/openssl/cipher.rb
+++ b/lib/openssl/cipher.rb
@@ -22,6 +22,8 @@ class Cipher
         }
       }
       const_set(name, klass)
+      deprecate_constant(name)
+      klass
     }
 
     %w(128 192 256).each{|keylen|
@@ -30,7 +32,10 @@ class Cipher
           super("aes-#{keylen}-#{mode}".downcase)
         }
       }
-      const_set("AES#{keylen}", klass)
+      name = "AES#{keylen}"
+      const_set(name, klass)
+      deprecate_constant(name)
+      klass
     }
 
     # call-seq:
diff --git a/lib/openssl/digest.rb b/lib/openssl/digest.rb
index 2ff8398e4..a784037df 100644
--- a/lib/openssl/digest.rb
+++ b/lib/openssl/digest.rb
@@ -24,7 +24,7 @@ class Digest
     #
     # which is equivalent to:
     #
-    #   OpenSSL::Digest.digest('SHA256', "abc")
+    #   OpenSSL::Digest.new("SHA256").digest("abc")
 
     def self.digest(name, data)
       super(data, name)
@@ -42,7 +42,10 @@ def self.digest(name, data)
         define_method(:hexdigest) {|data| new.hexdigest(data)}
       }
 
-      const_set(name.tr('-', '_'), klass)
+      constant_name = name.tr('-', '_')
+      const_set(constant_name, klass)
+      deprecate_constant(constant_name)
+      klass
     end
 
     # Deprecated.
diff --git a/test/openssl/test_digest.rb b/test/openssl/test_digest.rb
index 8d7046e83..836e03707 100644
--- a/test/openssl/test_digest.rb
+++ b/test/openssl/test_digest.rb
@@ -7,7 +7,7 @@ class OpenSSL::TestDigest < OpenSSL::TestCase
   def setup
     super
     @d1 = OpenSSL::Digest.new("MD5")
-    @d2 = OpenSSL::Digest::MD5.new
+    @d2 = EnvUtil.suppress_warning { OpenSSL::Digest::MD5.new }
   end
 
   def test_digest
@@ -54,10 +54,12 @@ def test_reset
   end
 
   def test_digest_constants
-    %w{MD4 MD5 RIPEMD160 SHA1 SHA224 SHA256 SHA384 SHA512}.each do |name|
-      assert_not_nil(OpenSSL::Digest.new(name))
-      klass = OpenSSL::Digest.const_get(name.tr('-', '_'))
-      assert_not_nil(klass.new)
+    EnvUtil.suppress_warning do
+      %w{MD4 MD5 RIPEMD160 SHA1 SHA224 SHA256 SHA384 SHA512}.each do |name|
+        assert_not_nil(OpenSSL::Digest.new(name))
+        klass = OpenSSL::Digest.const_get(name.tr('-', '_'))
+        assert_not_nil(klass.new)
+      end
     end
   end
 
@@ -118,14 +120,6 @@ def test_digest_by_oid_and_name_sha2
     check_digest(OpenSSL::ASN1::ObjectId.new("SHA512"))
   end
 
-  def test_openssl_digest
-    assert_equal OpenSSL::Digest::MD5, OpenSSL::Digest("MD5")
-
-    assert_raise NameError do
-      OpenSSL::Digest("no such digest")
-    end
-  end
-
   private
 
   def check_digest(oid)
diff --git a/test/openssl/test_ossl.rb b/test/openssl/test_ossl.rb
index e1d86bd40..b61140dd3 100644
--- a/test/openssl/test_ossl.rb
+++ b/test/openssl/test_ossl.rb
@@ -11,9 +11,6 @@ def test_fixed_length_secure_compare
     assert_raise(ArgumentError) { OpenSSL.fixed_length_secure_compare("aaa", "aa") }
 
     assert OpenSSL.fixed_length_secure_compare("aaa", "aaa")
-    assert OpenSSL.fixed_length_secure_compare(
-      OpenSSL::Digest.digest('SHA256', "aaa"), OpenSSL::Digest::SHA256.digest("aaa")
-    )
 
     assert_raise(ArgumentError) { OpenSSL.fixed_length_secure_compare("aaa", "aaaa") }
     refute OpenSSL.fixed_length_secure_compare("aaa", "baa")
diff --git a/test/openssl/test_pkcs7.rb b/test/openssl/test_pkcs7.rb
index d0d9dcaf8..0410dc604 100644
--- a/test/openssl/test_pkcs7.rb
+++ b/test/openssl/test_pkcs7.rb
@@ -117,7 +117,7 @@ def test_detached_sign
 
   def test_enveloped
     certs = [@ee1_cert, @ee2_cert]
-    cipher = OpenSSL::Cipher::AES.new("128-CBC")
+    cipher = OpenSSL::Cipher.new("AES-128-CBC")
     data = "aaaaa\nbbbbb\nccccc\n"
 
     tmp = OpenSSL::PKCS7.encrypt(certs, data, cipher, OpenSSL::PKCS7::BINARY)