The influence of static helical perturbations on high-energy ion motion in tokamaks is investigated. Numerical solutions of drift motion equations are in good agreement with analytic estimations of the critical amplitude value that is sufficient for destruction of drift surfaces. Three types of perturbations are considered: large-scale helical modes with wide regions of localization comparable with the plasma column radius, small-scale modes localized near the resonant magnetic surfaces, and balloon-like modes. For all three cases, high perturbation amplitudes are needed for destruction of drift surfaces. The static helical perturbation does not appear to lead to noticeable high-energy particle losses in tokamaks until the perturbation amplitude exceeds the value sufficient for magnetic surface destruction.