Both critical plane and stress invariant approaches are used to evaluate fatigue limit criteria of machine component subjected to non-proportional cyclic loading. Critical plane methods require finding the smallest circle enclosing all the tips of shear stress vectors acting on the critical plane. In stress invariant methods, the maximum amplitude of the second invariant of the stress deviator should be determined. In this paper, the previous algorithms for constructing the minimum circumscribed circle or hyper-sphere are briefly reviewed and the method using genetic algorithm is proposed.