Magnetohydrodynamic stability limits are determined for the ELMO Bumpy Torus. The relativistic hot electron annuli are considered to be rigid, modifying the magnetic field but not interacting with the instability. A modified energy principle is used, and the stability problem is reduced to determination of the eigenvalues of an ordinary differential equation along each field line. A threshold hot electron current is required for stability; its value agrees with experimental measurements. The calculations show that stable high .beta. equilibria are easily created.