Previous experiments [M. J. Coleman and A. Ruina, Phys. Rev. Lett. 80, 3658 (1998)] showed that a gravity-powered toy with no control and that has no statically stable near-standing configurations can walk stably. We show here that a simple rigid-body statically unstable mathematical model based loosely on the physical toy can predict stable limit-cycle walking motions. These calculations add to the repertoire of rigid-body mechanism behaviors as well as further implicating passive dynamics as a possible contributor to stability of animal motions.