The numerical prediction of three-dimensional melt filling and gas penetration in a clip-shaped square tube is conducted using a compressible model in this paper. The application of a finite volume discretization and volume-of-fluid method has been demonstrated to simulate three-dimensional gas-assisted injection molding processes. The modified Cross model and Tait Equation are implemented in the numerical scheme in order to describe the rheological properties of polymers. With the help of available experimental measurements, the numerical results of our three-dimensional compressible model are proven to have high prediction accuracy.