An apparatus for producing a parison having a plurality of resin layers and at least one resin layer of varying thickness is disclosed. The parison is used to form containers in a blow mold machine. An extruder is in communication with a flow head to form the parison. The apparatus includes a valve block having a duct providing communication between a second extruder and the flow head. Flow of resin from the second extruder directly to the flow head is controlled by a valve in the valve block. An accumulator cylinder and piston are also in communication with the duct and control the resin pressure within the duct. Opening and closing the valve and stroking the piston sends resin from the second extruder to the flow head and forms a resin layer having a varying thickness on the parison. A method of forming a varying layer is also disclosed.