Abstract: An efficient solution method,BI-CGSTAB,is extended and used to solve the linear algebraic system obtained from the discretization of the elliptic mild slope equation and to simulate the wave propagation over various topography with mild slopes.The numerical results show that the BI-CGSTAB method is efficient for solving the elliptic mild slope equation.The results obtained by the BI-CGSTAB method are much same as those obtained by other authors with different solution methods,but the convergent rate is much faster than that of other methods.