A port structure is provided for a container such as a flexible bag for I.V. fluids which will permit the piercing by a piercing pin in a leak resistant manner. The port structure is fabricated with the usual piercing diaphragm positioned in the innermost portion of the tubular port. Unlike the usual construction of port structures of this type, the inner tubular member containing the pierceable diaphragm is not connected to the remaining portions of the port structure at the outermost regions thereof or adjacent the flange or connecting portions, but instead joins the tubular member at an intermediary position so as to create a standing port for receiving the piercing pin.