Abstract: The problem of bulky memory requirement and low efficiency in calculation of unsteady flow with finite element method(FEM) has troubled the engineers for long time.It also restricts the applications of FEM to fluid dynamics The method of time-splitting and FEM were combined to solve the 2-D shallow water equations.The row-indexed sparse storage mode was used to store the sparse coefficient matrix,and the preconditioned bi-conjugate gradient method was used to solve the huge linear system.The results are satisfactory both in memory and efficiency The problem has been solved to a certain extent.