In this paper, we present parallel Poisson generators on N5/8×N3/8rectangular two-dimensional mesh-connected computers with multiple broadcasting (2-MCCMB's). The design of Poisson generators is based on the theory of the Poisson process and prefix computation. The time complexity of each generator is O(k/N7/8×N1/8) ,where k is the number of uniform random numbers used during the generation of the required Poisson numbers, and N is a power of two.