A rupture disc is a non-reclosing pressure-relief device actuated by inlet static pressure and designed to function by bursting a pressure-containing disc. It separates fluid from a safety relief valve, and thereby prevents leakage through the valve. Rupture discs are made from stainless steel, have a concave shape, and are designed to open at a predetermined pressure. They are used in safety-critical pressure-relief devices, and provide a leak-tight seal. In this paper, we describe a structural analysis and calculate the burst pressure of superficially grooved stainless-steel plate rupture discs. In general, rupture discs are designed based on a failure analysis of the material. We therefore conducted tensile tests on stainless-steel plate specimens to obtain their material properties, and then examined the relationship between the burst pressure and the thickness of the rupture disc using finite element analyses. Based on these results, we investigated the effects of groove depth and rupture disc thickness on burst pressure.