A polymer parison to be blow molded into a container configuration including a reduced diameter neck and a taper wall disposed between the neck and a greater diameter body portion of the container, which is shaped to permit a sufficient amount of stretch to be imparted to the taper wall forming portion of the parison which has a less-stretching tendency during the blow molding operation. Polyethylene terephthalate exhibits greatly improved characteristics and enhanced durability when it is biaxially stretched more than a certain fixed level. The parison is formed by injection molding such that when the parison is placed in the mold cavity, the taper wall forming portion is at an increased spaced distance away from the cavity wall so as to achieve a sufficient amount of stretch, as noted in the body forming portion of the parison, when it is blown to assume the contour of the mold.