A method and apparatus for welding thermoplastic materials with a stir welding system using a rotating element pin (307) or element with a geometry to induce frictional energy from the rotating element. A floating constraining surface (305) that has a motion independent of the rotation the pin (preferably stationary) is used to constrain ejection of material from the zone where the weld is being formed. Molten material is retained in the weld region, avoiding weakness and voids at the weld joint. Optionally a system (309) for introducing thermal energy into the weld zone in addition to the frictional energy is used. The system for introducing the thermal energy may be in association with the constraining shoe and/or the rotating tool, or a system independent of these.