A tubular plastic container having a molecularly oriented sidewall portion is made by bringing the peripheral portion of a solid blank in engagement with the shoulder portion of a die, introducing the blank into a cavity of the die while compressing with a first and second plungers, such that in the former stage of the introduction, the speed is relatively low and the pressure is relatively high, and then the speed is increased at a controlled rate and the pressure is decreased, thereby forming a hollow molded piece, and then expanding the molded piece to bringing the sidewall portion thereof into contact with the inner surface of the cavity.In the similar manner a tubular plastic container having a sidewall portion formed with thick wall portions axially extending and having a relatively large wall thickness and a large curvature, and thin wall portions axially extending and having a relatively small wall thickness and a small curvature which are formed alternately in the circumferential direction, is made by using the second plunger having recesses corresponding to the thick wall portions and having open edge portions.