Abandoning the assumption of nested magnetic surfaces in tokamak plasma expands the field of research and opens up new approaches for both theoretical and experimental plasma physics. The computer code KINX for calculations of the ideal MHD stability was developed for studies of doublet plasmas with two magnetic axes and using block-structured grids in each subdomain with nested magnetic surfaces. Then, the MHD_NX code on unstructured grids was developed to calculate the stability of two-dimensional equilibria with an arbitrary topology of magnetic surfaces. The study of equilibrium and stability of equilibrium configurations with toroidal current density reversal and axisymmetric n = 0 islands, which are associated with internal transport barrier and low current density at the magnetic axis, as well as with the operation of tokamaks in the alternating current regime, leads to more general issues of MHD stability of two-dimensional solutions of the Grad-Shafranov equations with islands under other types of symmetrychain of islands in helical symmetry and cylindrically symmetric m = 0 islands in configurations with the longitudinal field reversal. New ideal MHD unstable modes have been discovered for various types of two-dimensional island configurations. The energy principle with MHD-compatible boundary conditions at open magnetic field lines is necessary for the self-consistent stability analysis of divertor configurations in tokamaks with a finite current density at the separatrix, taking into account the plasma outside the separatrix. Several codes have been developed for calculations of plasma equilibrium and stability, taking into account the influence of currents outside the separatrix, which are ready for integration with other codes for edge plasma modeling.