A method is presented which can be directly applied to investigate the relation between Tokamak disruptions and the growing of the resonance amplitudes. Helical winding current thresholds for the destruction of magnetic surfaces in large aspect-ratio Tokamaks caused by interaction of different resonant fields are estimated. The radial dependence of the perturbations and the change in the shear over the island widths are taken into account. The magnetic surface break-up due to secondary islands caused by the coupling between the resonant helical fields and the toroidal curvature are also considered.