This paper presents an application of the Continuous Sensitivity Equation Method (CSEM) for the optimization of the injection molding process and its three-dimensional (3D) simulation by the finite element method. Finding the proper combination of process parameters such as injection speed, and melt and mold temperatures is critical to achieving a part that minimizes warpage and has the desired mechanical properties. Very often a successful design in injection molding comes at the end of a long trial and error process. Design Sensitivity Analysis (DSA) can help manufacturers improve their designs and can produce substantial savings in terms of both time and money. This work explores the ability of sensitivity analysis to predict the effects of design parameters on the performance of an injection molding process. The paper presents results of a 3D finite element solution of the filling stage of the injection molding process. Sensitivities of the solution with respect to different process parameters are computed using the continuous sensitivity equation method. Solutions are shown for the non-isothermal filling of a rectangular plate with a polymer melt behaving as a non-Newtonian fluid. The paper presents the equations for the sensitivity of the velocity, pressure and temperature and their solution by a finite element method. Sensitivities of the solution with respect to the injection speed, the melt and mold temperatures and to the heat transfer coefficient at the cavity/mold interface are shown.