Fluid mechanics plays an important role in many manufacturing processes including the pultrusion of composite materials. The analysis of fluid mechanics problems generally involves determination of quantities such as pressure and velocity. During the pultrusion process, the short, tapered inlet region of the pultrusion die experiences a significant amount of fluid resin pressure rise. The quality of a pultruded product can be affected by the amount of pressure rise in the pultrusion die inlet. Void formation can be suppressed and good fiber "wet out" achieved by a sufficiently high pressure rise in the pultrusion die inlet region. In this study the change in fluid resin pressure rise as a function of die entrance geometry is investigated by developing a finite element model based on the assumptions of Darcy＇s law for flow in porous media. The momentum equations are combined with the continuity equation to save computational time and memory. A Galerkin weighted residual based finite element method is developed to solve the resulting equation. This model is capable of predicting the pressure rise in the tapered inlet region of the pultrusion die as well as the straight portion of the die. By varying the size of the preform plates the thickness of the fiber/resin matrix approaching the die inlet can be varied. The finite element model predicts the impact of changing the preform plate size on the fluid resin pressure rise in the pultrusion die. The effect of varying the wedge angle for a linearly tapered die inlet region is also studied using this model. The results in this work can be useful for designing a pultrusion die system.