Recently, the conditions for stability of an arbitrarily shaped, finite-pressure toroidal plasma against localized ideal and resistive modes were presented. The characteristic time scale for local instability with respect to ideal modes is small compared with that for resistive modes so that an investigation of ideal local stability is a prerequisite for an assessment of non-ideal local stability. Here we consider the stability of a particular class of non-circular cross-section tokamak equilibria with respect to such modes. The equilibria are described analytically so that no ordering or expansion procedure is necessary, and both ideal and resistive stability are investigated over the whole plasma region. The effects of plasma shape (vertical elongation and triangularity), as well as aspect ratio are investigated and particular reference is made to next-generation tokamak designs (e.g. JET).