A resin transfer molding (RTM) process is disclosed for rapidly filling a fibrous preform and/or a rigid, porous body with high viscosity resin or pitch. The process is suitable for impregnated multiple porous bodies stacked in a single mold. The process uses a fibrous preform or rigid porous body which is placed into a mold matching the desired part geometry. A resin is injected into the mold at temperature and pressure. After cooling, the infiltrated component is removed from the mold. The mold is constructed from two halves fitted to form at least one mold cavity. A gate fitted with a nozzle is set into one of the mold halves, and a valve admits resin or pitch into the gate area. Venting or vacuum can be applied to the mold. The mold is held in a hydraulic press and an extruder, optionally fitted with an accumulator, supplies molten resin or pitch to the mold.