We present results from a numerical investigation of the localization of deformation in thin elastomeric spherical shells loaded by differently shaped indenters. Beyond a critical indentation, the deformation of the shell ceases to be axisymmetric and sharp structures of localized curvature form, referred to as “s-cones,” for “shell-cones.” We perform a series of numerical experiments to systematically explore the parameter space. We find that the localization process is independent of the radius of the shell. The ratio of the radius of the shell to its thickness, however, is an important parameter in the localization process. Throughout, we find that the maximum principal strains remain below 6%, even at the s-cones. As a result, using either a linear elastic (LE) or hyperelastic constitutive description yields nearly indistinguishable results. Friction between the indenter and the shell is also shown to play an important role in localization. Tuning this frictional contact can suppress localization and increase the load-bearing capacity of the shell under indentation.