A blow pin assembly for a rotary blow molding machine having a carrousel that supports a number of molds located about the circumference of the carrousel. Each mold includes a separate blow pin assembly mounted on the mold clamp. The blow pin assemblies each includes a base, a carriage supported by the base, a sub-base supported by the carriage, and a blow pin mounted to the sub-base for movement therewith. The carriage moves the sub-base and blow pin linearly along a first path from a home position, in which the blow pin is retracted away from the mold opening, to an alignment position, in which the blow pin is located directly above the mold opening. The sub-base then moves the blow pin in a direction perpendicular to the first path from the alignment position into a mold-engaging position, in which the blow pin is inserted into the mold opening. This sequential, orthogonally-related motion allows the blow pin to be retracted away from the mold opening during the parison extrusion operation, yet permits the blow pin to enter the mold opening along a linear path that is coincident with the central axis of the mold. This motion permits pre-blowing of the blow pin and helps minimize the opportunity for the blow pin to catch and fold over the upper edge of the parison. The blow pin assembly can include a pair of stop members that positively engage each other when the blow pin has reached its alignment position.