Abstract: There are described a method ultrasonically connecting, in overlapped relationship, a number of so-called processed paper sheets having coatings of a thermoplastic, synthetic resin material or a number of film sheets each consisting of a continuous phase of a thermoplastic, synthetic resin material and a dispersed phase of an inorganic material. The sheets to be connected are placed between a working table and an ultrasonic vibrator at least one of which has a surface configuration complementary to variations in thickness of the overlapped welding sheet portions, for uniformly distributing the ultrasonic vibratory energy and static pressure to the entire area of the overlapped sheets to preclude scorches which would otherwise be developed internally in particular localities of the overlapped sheets due to uneven distribution of the applied static pressure and the vibratory energy.