A linear resistive magnetohydrodynamic (MHD) stability analysis of a finite beta, cylindrical reversed field pinch (RFP) plasma is presented. The equilibrium distributions are specified by a model describing both the parallel and the perpendicular current density components. The average beta (⟨β⟩) of the configurations is varied by using the parameter χ (0 ≤ χ ≤ 1) which ensures that Suydam's necessary condition for stability is satisfied. It is found that there are configurations which are stable with respect to ideal pressure driven modes at rather high ⟨β⟩ values (up to 30%), although small changes in the equilibrium can produce a drastic reduction in the maximum achievable beta value. In this model, in which viscosity and Hall term effects are not taken into account, resistive g-modes are in general found to be always unstable, independent of the beta value. However, by considering only modes with 'sufficiently' high growth rates, it is possible to deduce some stability boundaries and 'beta limits' for relatively low values of the magnetic Reynolds number.