The stability against resistive tearing and interchange modes for an inviscid incompressible plasma confined by a resistive rigid wall is studied. The limiting case of a non conducting rigid wall is also examined in some detail. Results for equilibrium configurations of the reversed field pinch type are presented for both cases. In particular the high beta pitch and pressure model and experimental profiles for the Eta Beta II RFP are considered and the results are compared with the classical (i.e. infinite conducting wall) case.