The apparatus comprises a melting chamber (6) in communication with a molding cavity made up by two half-molds (1, 2) in a close position, an inlet duct (3) through which plastic material is fed into said melting chamber (6), an ultrasound vibration element (4) activated by an ultrasound generator (5) and provided with an end portion inserted in the melting chamber (6) through an access opening thereof, and motion means for generating a relative displacement between the ultrasound vibration element (4) and the melting chamber (6). The ultrasound vibration element (4) is supported by adjustment means so as to adjust the position of a longitudinal axis (E) thereof in two cross directions (X, Y) perpendicular to each other and perpendicular to an axial direction (Z) parallel to a longitudinal axis of the melting chamber (6).