AbstractBased on Barone and Caulk's model and a generalized variational functional, a finite element simulation was developed for the compression molding of thin and thick parts. For solving theu‐v‐ptype equations, an element‐based penalty method and a mixed formulation were implemented. Numerical results show that the new model gives better accuracy in velocity and velocity gradient than the Hele‐Shaw formulation for cases where both models are appropriate. Predictions of velocity and its gradient by the model are compared with other FEM results and BEM solutions. Using a fixed base mesh that covers the mold cavity, a new technique was developed for tracking the moving flow front. Temporary elements and nodes are generated for the filled part of elements intersected by the flow front. This method allows a smooth representation of the flow front and has exact boundary conditions on the flow front. The scheme is demonstrated for compression molding of an elliptical and an L‐shap