Elliptic partial difference equations like Poisson's equation are used in many fields of application. However, the coefficientmatrix of the derived algebraic equation is large and sparse, and so its inversion is expensive. Various iterative methods are used to solve such a sparse matrix system. Although there have been many studies on solving the large sparse matrix system [1, 2, 3, 4, 5, 6, 7], there have been few reports on the implementation and performance of the iterative method with multicolor ordering. In this paper, a novel implementation technique to enhance the performance of the 2-colored SOR method is proposed, which eliminates the recursion for the standard 7-point stencil on the Cartesian grid in three dimensions. The performance of the multicolor SOR method is investigated on both a shared memory vector/parallel computer and a symmetric multiprocessor machine in a distributed memory environment.