By providing a high speed welding system (27) for fusing adjacent foam profiles (21) in a continuous manufacturing operation (20), a unique, integrated, foam welding and profile manufacturing system is attained which is capable of producing virtually any desired foam product (22) from foam extrusions without requiring the use of expensive molds or forming components, and which significantly reduces expensive scrap found in prior art construction systems. In accordance with the teaching of the present invention, any desired cross-sectional shape or configuration is capable of being manufactured in fully automated, high-volume, rapid production conditions, with virtual ease and simplicity. Furthermore, by employing the present invention, foam profiles which previously were unattainable due to their structural configurations, are quickly and easily constructed in a mass production operation.