An improved and mechanically simplified blow head mechanism for blowing a parison and internally cooling the blown parison is disclosed which may be used with an I.S. machine to blow a parison to form a glass container and then internally cool the blown parison below the annealing point. The blow head mechanism has a cooling tube which supplies final blow and cooling air and which is raised or lowered by raising or lowering the blow head mechanism. The blow head mechanism supports a blow head with a pressurized cylinder which maintains the blow head in a position in engagement with the finish of a parison once initially lowered irrespective of the blow head mechanism being further lowered to lower the cooling tube into the blown parison.