[en] Results are presented of a parametric study of the ideal magnetohydrodynamic stability properties of the spheromak, or compact torus, configuration. In the absence of a nearby conducting wall, the spheromak is always unstable to at least one current driven mode. With a conducting wall at the surface, the spheromak can be unstable to current driven modes if the current is too peaked, i.e., q/sub o/(R/a) less than or equal to 2/3, or if the shear is too low at the origin. The Mercier criterion sets an upper limit on the pressure gradient everywhere, but configurations that are everywhere Mercier stable can be unstable to pressure driven low-n modes. Stable toroidal configurations exist with a spherical wall separated by half a minor radius, and with β/sub theta/ = 30%