A hybrid 3D/2D finite element method is proposed to simulate polymeric fluid motions for various polymer processing operations that may involve complex flow geometries. The flow regime is divided into 2D and 3D regions, and the fluid flow is assumed to follow the Hele Shaw model in the 2D region. Mathematically the 2D and the 3D regions are linked by the conservation of mass and the continuation of pressure variations. Two example calculations have been used to illustrate the accuracy and efficiency of the new numerical technique, and it was found that a substantial amount of computing time can be saved to obtain numerical solutions that are as accurate as the complete 3D calculations.