An activation rupture disc unit is provided that is capable of withstanding a substantially higher back pressure than its burst activation pressure. The unit includes a tubular housing having a fluid passage. Tapered wall structure defines at least a portion of the passage with the fluid outlet thereof being of greater area than the fluid inlet. A rupture disc is carried by the housing and has a central bulged section in fluid-blocking relationship to the passage. A tapered, self-releasing solid plug is positioned in and conforms to the tapered portion of the passage. The plug has a curved surface conforming to and positioned in full supporting relationship to the central section of the rupture disc. The plug is of sufficient mass to prevent rupture of the central section of the disc under a back pressure substantially greater than the activation pressure of the disc.