The quest to determine accurately the stability of tearing and resistive interchange modes in two-dimensional toroidal geometry led to the development of the PEST-3 code, which is based on solving the singular, zero-frequency ideal MHD equation in the plasma bulk and determining the outer data Delta', Gamma', and A' needed to match the outer region solutions to those arising in the inner layers. No assumptions regarding the aspect ratio, the number of rational surfaces or the pressure are made a priori. This approach is numerically less demanding than solving the full set of resistive equations and has the major advantage of allowing for non-MHD theories of the non-ideal layers. Good convergence is ensured by the variational Galerkin scheme used to compute the outer matching data. To validate the code, we focus on the growth rate calculations of resistive kink modes which are reproduced in good agreement with those obtained by the full resistive MHD code MARS. (C) 1994 Academic Press, Inc.