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The simulations of flow, heat transfer and reaction kinetics during the compression molding of thin three-dimensional parts are possible by a new numerical model based on a moving boundary condition for the drag motion of an upper mold of a non-planar shape or for the apparent slipping events of particle filled materials. The part thickness and the mold closing velocity influence the gap-wise distributions of the temperature and degree of cure. The flow pattern is affected by the moving boundary conditions and the degree of cure is affected by temperature.