Three-dimensional, ideal MHD tokamak equilibria are computed with the free-boundary NEMEC code, and their stability properties are investigated with the CAS3DN code, which is an ideal, linear MHD code. Numerical problems are discussed in detail by means of a test equilibrium with a large helical core. Further computations are performed for AUG-type equilibria perturbed by resonant magnetic perturbation (RMP) fields, and an ITER scenario taking into account the toroidal field ripple and perturbation fields caused by test blanket modules (TBMs). Moreover, a quantitative measure of the corrugation of the flux surfaces is introduced. It is found that the contour of the corrugation on equilibrium flux surfaces reflect the ideal kink structures of rational-q surfaces, and the periodicity of the external perturbation fields. Both stabilizing and destabilizing effects of the RMP fields, and the influence of the TBMs on the stability properties are observed.