Non-fragmenting pressure relief apparatus includes at least one circular rupture disc having a central asymmetric bulged section and a peripheral flange portion. A semi-circular line of weakness extends around the periphery of the bulged section and presents a hinge portion between the ends of the line of weakness. A hold-down member for the rupture disc having an inner opening surrounding the bulged section of the disc is provided with a unitary segment that extends into the inner opening of the hold-down member. The spaced end extremities of the line of weakness extend beneath the hold-down member segment. The hinge portion of the disc upon rupture of the disc bends about a fulcrum defined by the outer margin of the hold-down segment, which in conjunction with deflection of the segment of the hold-down member contributes to anti-fragmentation of the disc.