Injection molding, parts onto a carrier web (34) located between mold halves (18,20). Flow of polymer melt into the mold is assisted by application of ultrasonic energy to the mold cavity. After the molding operation, mold halves are separated, and the carrier web is advanced, or indexed, to a next position for another molding sequence. Molding apparatus comprises a moving mold face (20), that can move toward and away from a first mold member (18) (which can be stationary) in which the mold cavity is located, a means (24,25,26,30,32) for moving and/or indexing carrier web between the first mold member and the moving mold face, means (16) to inject polymer melt into the mold cavity, and an ultrasonic system (42) providing ultrasonic energy to the mold cavity. The carrier web can transport molded parts to subsequent process steps, such as coating, drying, inspection, curing, assembly or packaging.