Abstract: A new numerical method for solving two phase air-water flow equations is developed The two phase air-water equations are solved with a finite element method.A discrete Newton iterative method is adopted to linearize the non-linear finite element equations after temporal and spatial discretion,it not only converges faster than the other methods,but also avoids the difficulties on programming.The mean of paralleling is adopted to solve the two-phase finite element equations,reducing much EMS memory needed in calculation by integrating means.