The two-dimensional Burgers' equations are discretized in fully implicit finite-difference form. This scheme leads to a system of nonlinear difference equations to be solved at each time-step. Newton's method is used to solve this nonlinear system. The linear system is solved by a direct method at each iteration of Newton's method. The accuracy of the proposed numerical scheme is examined by comparison with other analytical and numerical results. The present method performs well. (C) 2002 Published by Elsevier Science Inc.