A physically accurate and computationally effective pure finite-element-based methodology for Resin Transfer Molding (RTM) process simulations is presented. The formulations are developed starting with the time-dependent mass conservation equation for the resin flow. Darcy's flow approximations are invoked for the velocity field, thereby forming a transient governing equation involving the pressure field and the resin saturation fill factor which tracks the location of the resin front surface. Finite element approximations are then introduced for both the fill factor and the pressure field, and the resulting transient discrete equations are solved in an iterative manner for both the pressures and the fill factors for tracking the progression of the resin front in an Eulerian mold cavity. The formulation involves only a pure finite-element Eulerian mesh discretization of the mold cavity and does not require specification of control volume regions and has no time increment restrictions that exist as in the traditional explicit finite-element-control volume based formulations. The present formulations accurately account for and capture the physical transient nature of the mold-filling process while maintaining improved numerical and computational attributes. Mold-filling simulations involving various geometrically complex mold configurations are presented, demonstrating the applicability of the developments for practical manufacturing process simulations.