Departures of the geometry of the middle surface of a thin shell from the perfect shape have long been regarded as the most deleterious imperfections responsible for reducing a shell’s buckling capacity. Here, systematic simulations are conducted for both spherical and cylindrical metal shells whereby, in the first step, dimple-shaped dents are created by indenting a perfect shell into the plastic range. Then, in the second step, buckling of the dented shell is analyzed, under external pressure for the spherical shells and in axial compression for the cylindrical shells. Three distinct buckling analyses are carried out: (1) elastic buckling accounting only for the geometry of the dent, (2) elastic buckling accounting for both dent geometry and residual stresses, and (3) a full elastic–plastic buckling analysis accounting for both the dent geometry and residual stresses. The analyses reveal the relative importance of the geometry and the residual stress associated with the dent, and they also provide a clear indicator of whether plasticity is important in establishing the buckling load of the dented shells.