A computer program to simulate three dimensional flow in injection molding process has been developed. To investigate numerical methods of moving free surfaces of the flow, the flow in injection molding process is regarded as isothermal, incompressible, high viscous flow of a Newtonian fluid with free surfaces. Generally, many computing times and computer memories are spent for numerical calculation of high viscous flow with free surfaces. Therefore, an effective combined calculation method was developed by using the two‐stages rational Runge–Kutta scheme for time integration, the pseudo concentrations method for calculation of the moving free surfaces and the donor‐acceptor scheme for an advection equation of the pseudo concentrations to reduce the computational effort in the computer program. A numerical calculation was carried out for the mold filling simulation in a cavity composed of a plate and a cylinder. This calculated result was compared with the experimental result which was obtained by an observation of filling flow of silicone oil in a visible cavity. As a result, the calculated flow patterns agreed with the observed ones.