A process, and the product thereof, for making a composite vessel having at least one closed end, the process including the steps of: fabricating a thermoplastic liner for the vessel; overlaying onto the liner a layer of commingled fiber and thermoplastic material to obtain a composite intermediate structure; pressing and heating the composite intermediate structure to effect at least partial consolidation in apparatus which includes upper and lower silicon rubber bags, the bags having dimensions such that, during operation, their facing peripheral regions abut to encompass the composite intermediate structure; then placing the composite intermediate structure in a mold; heating the composite intermediate structure in the mold while applying a force, such as internal gas pressure, tending to urge the composite intermediate structure against and into the shape of the interior walls of the mold until the thermoplastic liner and the overlaid layer fully consolidate; cooling the mold and composite vessel until the composite vessel is solidified; and removing the formed composite vessel from the mold. The commingled fiber and thermoplastic material may either be wound onto the liner or laid on the liner in the form of fabric woven from the fiber and threads of the thermoplastic material.