The equilibrium of a class of field‐reversed configurations in an external magnetic field is studied analytically. Bifurcation points in parameter space appear when the elongation of the separatrix is equal to 1.61 or to 0.23. In general, for fixed parameters, two equilibria are possible, one of which is almost spherical while the other is highly prolate or, alternatively, highly oblate. The nearly spherical equilibrium corresponds to a lower energy condition.