In this thesis, an analysis of MD5 and MD6 algorithms is made along with their comparison to other known hash algorithms. A cryptographic hash function is a function that converts a variable-length input message into a fixed-length string. The result is called hash or message digest. It is most commonly used to check message integrity or for storing passwords. Other properties are that it must be fast, it always has to generate the same hash for the same input, and that the two different messages can't have the same hash value. The quality of the hash function is measured by its resistance to collisions and various types of attacks. Hash functions are divided into MDC (without-key) or MAC (with-key) and can be created by using Merkle-Damgård construction, (fast) wide-pipe construction, or sponge construction. MD5 is a well-known hash algorithm used to check message integrity. It converts input to a 128-bit hash by dividing the message into 512-bit blocks, which are then processed through four rounds in which the four main nonlinear functions are used.