The interchange (Mercier) stability of toroidal reversed field pinch plasmas with non-circular cross-section has been evaluated numerically. Marginally stable pressure profiles and beta values have been produced. Most shapes, such as indented or vertically elongated, reduce the stability by making the net magnetic curvature of the poloidal field dominated plasmas yet worse than that of circular configurations. The stability of horizontally elongated plasmas is slightly enhanced compared with that of circular plasmas as a result of increased shear produced by toroidicity. This shear enhancement by toroidal shift of magnetic surfaces might be exploited in future, more comprehensive studies.