Abstract An efficient and simple parallel SOR iterative algorithm is presented for the finite difference and finite element methods. Based on domain subdividing and computing sequence reordering, this algorithm has been proven to be efficient and simple to implement. No coloring scheme and no overlapping blocks are required. With this parallel algorithm, not only computations for the mesh points in the subdomain but also computations for the mesh points on the inferace are carried out parallely. In addition, programming efforts to implement the parallel algorithm are simplified. When compared with the results using the conventional sequential algorithm, excellent efficiencies are obtained using the parallel algorithm.