Ellipsoidal and torispherical heads, whose geometric shapes are close, are usually used as end closures of internally pressurized vessels. In pressure vessel codes, for example, ASME BPVC Section VIII and EN13445-3, ellipsoidal heads are designed as torispherical heads using geometric equivalency approaches. However, the difference between ellipsoidal and equivalent torispherical heads has not been studied in detail. In this paper, we first investigate shape deviation between the two types of heads. Then we compare elastic–plastic behaviors between ellipsoidal and equivalent torispherical heads as well as their failure modes, i.e., buckling and plastic collapse (bursting). It is found that ellipsoidal heads have more buckling resistance than equivalent torispherical heads, indicating that the current design rules for buckling of ellipsoidal heads based on the geometric equivalency approaches result in uneconomical design. In addition, experimental and numerical results show that such heads experience geometric strengthening. The finite element (FE) method considering the effect of geometric strengthening provides a good prediction of plastic collapse pressure. However, the current design equation for bursting does not consider the effect of geometric strengthening, also leading to uneconomical design. Therefore, in order to avoid uneconomical design, we recommend that (1) with respect to buckling of ellipsoidal heads, a new design equation be proposed rather than implementing the geometric equivalency approaches, and (2) the current design equation for bursting be deleted, and a new design equation, considering the effect of geometric strengthening, be proposed for bursting of ellipsoidal and torispherical heads.