Cryptography is the art of providing security to the message .It gives freedom to the user from hacking of the original message. The here are multiple techniques to provide cryptographic security to the message but this paper focus on the SHA-256 hash function and its extended proposed model SHA-288 for better security. The basic structure of maximum hash functions is based on the Merkle- Damgard construction. Most of the hash functions are used for information security purposes such as digital signature, password authentication; message authentication etc.The hash algorithms perform security checks over plain text by converting plain text into cipher text called message digest or checksums. The paper explains about the cryptanalysis and design of SHA-2 Family as MD5 and SHA-1 going to be outdated after few months. The new model based on construction of SHA-256 has also been highlight for providing strength to the security domain.