The ideal and resistive MHD free-boundary stability of m = 0, 1, 2 and 3 modes is calculated for the circular force-free reversed field pinch (RFP). Functions μ(r)= μ0·/B2 specifying the equilibrium configurations are chosen to approximate the deviations of experimental RFPs from the fully relaxed state. Families of unstable modes are identified. All are resistive in the usual RFP parameter range, unless the distance to the conducting shell is very large. The usually stable m = 2 and 3 modes, as well as m = 0 and m = 1, are unstable near the plasma edge for practical shell separations, and these modes might promote greater edge relaxation than if plasma and shell were in contact. When a small central peaking of μ(r) is present, the unstable mode spectrum hardly varies as the shell is moved outward. It is suggested that extreme closeness of the shell to the plasma might not be required. Moderate plasma-shell separation might also eliminate sawtoothing at high reversals. Supporting evidence from OHTE and HBTX 1C experiments is cited.