Nonlinear shallow shell equations are derived for a thin shell of revolution having the shape of a narrow segment of a toroidal shell centered at the equator. The equations are derived by considering a cylindrical shell, described by nonlinear Donnell theory, with an initial radial deformation. Linear buckling equations are obtained by perturbing the nonlinear shell equations. The buckling equations are solved for the case of a simple supported equatorial segment of a spherical shell loaded in the axial direction by its own weight. Plots are presented which compare a critical thickness parameter with the results of an elementary approach. The elementary approach assumes that the shell will buckle if the maximum compressive stress is greater than the critical compressive stress for a complete sphere loaded by uniform external pressure. / M.S.