Hash functions have a very important role in network and telecommunication security. These functions play an important role in hashing a message which are widely used in cryptographic applications such as digital signatures, random number generator algorithms, authentication protocols, and so on. Rotational cryptanalysis is a relatively new attack that is part of a generic attack on hash functions and is effective on algorithms that have an ARX structure. In this paper, for the first time, we apply a rotational cryptanalysis and with the given assumption of the markov chain for the modular additions sequence employed in two algorithms Shabal and CubeHash, which are second-round candidates for the SHA-3 competition that use the ARX property in their structure. With the implementation of rotational cryptanalysis we arrived at the complexity of 2-3393. 58 for the entire 16+3-rounds Shabal algorithm and the complexity of 2-57. 6 for the en-tire 16-round CubeHash algorithm. According to the obtained results, it can be seen that due to the large number of modular additions with the given assumption of markov chain, the Shabal algorithm exhibits greater resistance to rotational cryptanalysis, compared to the CubeHash algorithm and is less likely to succeed.