This paper presents a finite element solution algorithm to solve polymer injection molding problems. The methodology solves the momentum, mass and energy conservation equations in three-dimensions. Packing and cooling stages of the injection molding process are modeled by considering compressibility effects. The procedure is aimed at processes in which three-dimensional effects are important. The method is also shown to be effective for thin parts. The performance of the proposed approach is measured on the injection of a plate for which experimental data are available. The procedure is also applied to a thick 3D part. The method results in accurate solutions and it is a useful tool to quantify, the material behavior on cases otherwise difficult to investigate.