A parallel variant of the block Gauss-Seidel method is presented to solve the Poisson equation with Dirichlet boundary condition. This method uses two-dimensional logically connected parallel processors. Furthermore, natural rowwise (NR) data flow block ordering is used so that its convergence rate is the same as that of the standard block Gauss-Seidel method. Spectral radius is determined by the formula for general k x I block iterative methods. Numerical computations on a parallel computer are included. (C) 1999 Published by Elsevier Science Inc. All rights reserved.