High toroidal mode number, magnetohydrodynamic perturbations of a plasma confined in an axisymmetric field‐reversed geometry with no toroidal field can be stabilized by the presence of a ring of energetic, large‐orbit ions. Analytical and numerical studies reveal that high‐&bgr; plasma stability against ballooning and interchange modes improves as the ring current profile becomes more peaked. The equations of motion for incompressible mode perturbations in the vicinity of the vortex point are solved analytically to obtain the ballooning stability conditionF>(1+‖&egr;‖)/2, whereFis the fraction of the current density carried by the ring ions and &egr; is the flux surface ellipticity. Higher‐order corrections to the eigenfrequencies due to compressional effects are obtained in the limit of circular flux surfaces. Modeling the ring as an exponential rigid rotor, an iterative procedure is used to obtain optimal values ofEp/Eb, the ratio of the total energy of the confined plasma to the total ring energy. Magnetohydrodynamically stable equilibria are found withEp/Eb≲2.