The elastic-plastic buckling of internally pressurized torispherical shells is considered in some detail in the paper. The effects of geometric parameters (r/D, RS/D and D/t) and material properties (σyp, E and the strain-hardening coefficient) on the elastic-plastic internal buckling pressures were investigated using the BOSOR 5 program. Based on the results of the parametric study, approximate formulas for predicting the elastic-plastic internal buckling pressures are suggested. These should be useful to designers.