As an important cryptographic criterion of Boolean function, algebraic degree is widely used in the design and analysis of ciphers. This work mainly studies the algorithm for estimating algebraic degree of Boolean function and its applications to SIMON-like ciphers. Firstly, by analyzing the algorithm of using truth table to solve algebraic normal form, a parallel solution architecture based on CUDA is constructed. The model uses the CPU and GPU computing resources collaboratively, which greatly reduces the time for solving algebraic degree. As applications, the algebraic degree of full round function is solved for SIMON32 and SIMECK32 in a short time. Secondly, based on the Cube attack theory, a probabilistic algorithm for estimating algebraic degree is presented according to the relationship between algebraic degree and superpoly. The algorithm is applied to estimate algebraic degree of general SIMON-like ciphers. Finally, from the algebraic degree point of view, the differences of SIMON-like ciphers selecting different cyclic shift parameters are given, and then some design choices for cyclic shift parameters are proposed. The experiment shows that SIMON has shortest number of required rounds to reach maximum algebraic degree under original parameters, thus means that the original parameters have higher security.