A rigorous solution (generalized Lorenz-Mie theory) and an approximate solution (geometrical optics) are developed for the optical stress distribution on the surface of a homogeneous sphere. Demonstration calculations are made for plane-wave and Gaussian-beam illuminations. The influence of diffracted waves, surface waves, interference effects, caustic points, beam width, and refractive index on the stress is analyzed. The Debye series is used to evaluate the validity of geometrical optics and provides a quantitative analysis of the contribution of rays of different orders.