The stress-strain behaviour in the notch tip of elastic-plastic bodies is discussed in the presentation. The approach is based on the incremental formulation which relates hypothetical elastic energy density to elastic-plastic energy density at the notch root. The Mróz-Garud multisurface cyclic plasticity theory is employed for simulation of the material response due to the current load increments. The equations of the energy density balance in the notch root together with constitutive relations formulate a set of algebraic equations. The fictitious elastic load history at the notch root and the material constitutive relations provide the parameters, so that the set of equations can be easily solved for the stress and strain increments. A shaft with a circumferential notch subjected to random load events is addressed to as an example of a component specified to predict the material stress-strain behaviour. The calculation results, obtained for general non-proportional load paths, are compared to the corresponding finite element data.