A blow molding machine capable of relatively high production rates at relatively low cost is provided. The blow molding machine comprises a base, a reciprocating shuttle mechanism supported by the base, a single blow molding station supported by the base, and adapted to receive a parison for forming the hollow article at the blow molding station, a pair of cooling stations supported by the base on flanking sides of the blow molding station, a pair of blow pin carriages spaced from one another, each of which is connected to the shuttle mechanism and is indexable to the blow molding station and to one of the cooling stations. Each blow pin carriage can comprise one or more blow pin assemblies that are movable independent of the shuttle mechanism between a rest position and a blow position.