<p><b>Abstract</b>—An analytical expression has been obtained for estimating the destructive pressure of gas within a closed spheroidal pore with a crack emanating from the pore surface. The approach of linear elastic fracture mechanics (LEFM) has been used. The destructive pressure, defined by Irwin’s brittle fracture criterion, depends on both the sizes of the pore and the crack, as well as the shape of the pore itself. As an example, calculations are provided for steel with 0.5% C and 1% Cr and ceramic Al₂O₃. The destructive pressure in the pore as a function of radius and shape of the pore and of the size of the crack is constructed. It is shown that for steel there is a limiting pore size below which gas-filled pores with cracks are safe in terms of crack resistance, provided there are no external loads. The limitation on the plastic zone at the tip of the crack (LEFM) for steel restricts the legitimacy of the presented calculations of destructive pressure according to Irwin’s criterion to crack sizes <i>l</i> ≥ 2.3 mm and, consequently, to pore sizes <i>a</i> &gt; 2.3 mm.</p>