  In this paper we consider the numerical approximation of the two-phase
membrane (obstacle) problem by finite difference method. First, we introduce
the notion of viscosity solution for the problem and construct certain discrete
nonlinear approximation system. The existence and uniqueness of the solution of
the discrete nonlinear system is proved. Based on that scheme, we propose
projected Gauss-Seidel algorithm and prove its convergence. At the end of the
paper we present some numerical simulations.
