A cap adapted for use as a container cover where the cap has a thermoplastic resin liner pressed formed onto the inner surface of a cap shell. The plastic liner is formed such that the difference between the intrasurface orientation index of the outer peripheral portion of the liner and the intrasurface orientation index of the central portion of the liner does not exceed 0.37 where the intrasurface orientation index is defined as the sum of the orientation coefficient of the liner in the radial direction and the orientation coefficient of the liner in the circular direction.A method of making a cap having a thermoplastic liner where the liner is press-formed into shape under conditions whereby the difference between the intrasurface orientation index of the outer peripheral portion of the liner and the orientation index of the central portion of the liner does not exceed 0.37.