In this paper the finite element method is employed to solve the streamfunction vorticity formula for viscous incompressible fluid flowing past two dimensional backward facing step. The vorticity on the solid wall are determined by the method of time iteration, without using the first order or second order accuracy of wall vorticity formula. We calculated the values of streamfunction and vorticity on the domain at Re=200, 400, 800 and 1000, and we compare our results at Re=800 with others, it is very agreement with each other. The effect of output boundary conditions on the computing results is also studied. The method used here is valuable to analyze the flow at the port of hydraulic valves.