The authors present a method for calculating multiaxial elastic-plastic stresses and strains in notched bodies subjected to proportional and non-proportional loading histories. The method is based on an incremental formulation relating the hypothetical linear elastic and elastic-plastic strain energy densities at the notch tip. The material stress-strain behavior is simulated according to Mróz-Garud cyclic plasticity model. Each formulation consists of a set of incremental algebraic equations that can easily be solved for elastic-plastic stress and strain increments if the increments of the hypothetical elastic notch tip stress history and the material stress-strain curve are known. It is found that the generalized Neuber rule which represents the equality of total strain energy densities at the notch tip, gives an upper bound for elastic-plastic notch tip strains. The method is verified by comparison with finite element data obtained for non-proportional loading path for nonlinear stress-strain material model. The method is particularly suitable for fatigue life analysis of notched bodies subjected to multiaxial cyclic loading paths.