The onset of plastic yielding in a spherical shell loaded by a rigid flat is analyzed using finite element analysis. The effect of spherical shell geometry and material properties on the critical normal load, critical interference, and critical contact area, at the onset of plastic yielding, is investigated and the location where plastic yielding first occurs is determined. A universal dimensionless shell parameter, which controls the behavior of the spherical shell, is identified. An empirical relation is found for the load-interference behavior of the spherical shell prior to its plastic yielding. A limiting value of the dimensionless shell parameter is identified above which the shell behaves like a solid sphere.