This paper presents two parallel algorithms to compute reversal distance of two signed permutations on different models. These two algorithms are based on Hannenhalli and Pevzner's theory and composed of three key steps: Construct break point graph, compute the number of cycles in break point graph and compute the number of hurdles in break point graph. The first algorithm runs in O(log²n) time using O(n²) processors in SIMD-CREW model. The second one can solve the problem in O(logn) bus cycles by using O(n³) processors on the linear array with a reconfigurable pipelined bus system (LARPBS).