The boolean satisfiability problem SAT is one of the fundamental and open tasks in present-day information science. This problem is NP-complete. It means that all N P problems can be reduced to SAT in polynomial time. Interestingly, among NP problems, there are many closely related to cryptology, for example: factorization of numbers – important for RSA, breaking keys of symmetric ciphers, finding collisions of hash functions and many others. The discovery of the polynomial algorithm for SAT would result in resolving one of Millennium Prize Problems: P vs. N P. This objective seems to be hard to achieve – it’s unknown if it is even possible. With slightly lower aspirations, we can design heuristic or random algorithms for SAT. Therefore, the main goal of our study is to present a project of parallel SAT Solver based on WalkSAT algorithm, including its implementation using the OpenCL programming environment and a computer equipped with NVIDIA Tesla graphics cards. With the rapid development of GPU technology and FPGAs, as well as portability of solutions created in OpenCL, the direction of such works becomes interesting because of computational efficiency gained, as well as solution prototyping rate.