A method for assembling at least two rigid thermoplastic material based parts. The two parts are superposed to have at least one interface zone, wherein at least one of the two parts includes one or plural energy directors, protruding, situated in the interface zone. At least one excited ultrasonic source is brought into contact with one of the two parts, the ultrasonic source applying a compression effort to the two parts in a region of the interface zone located opposite the ultrasonic source. The ultrasonic source is continuously displaced at the interface zone to form a continuous welded joint by fusion of the thermoplastic material in the region positioned opposite the ultrasonic source. Such a method may find particular application for assembly of stratified parts.