A method of friction welding thermoplastic materials, such as a reinforcing plate to the inner surfaces of oppositely disposed legs of a generally U-shaped workpiece, wherein a flexible force applying means applies a force in a direction normal to the direction of relative motion between the parts but in the plane of the mating surfaces for urging the legs of the U-channel into intimate contact with the edges of the reinforcing plate. During a weld time interval the parts undergo relative linear reciprocating motion while being urged in intimate contact by the flexible force applying means which causes the mating surfaces to soften under the influence of friction. After the weld interval, the parts are returned to their original position and are held in forced contact for a time sufficient for the mating surfaces to solidify. Upon solidification the force ceases and the welded parts are removed from the apparatus.