A multiaxial local stress-strain approach based on the Armstrong-Frederick type cyclic plasticity theory was proposed to perform the stress analysis and the fatigue analysis on the notched components. A robust cyclic plasticity model was adopted to describe the non-Masing behavior of 16MnR steel. The incremental form of the multiaxial local stress-strain approach was formulated with the incremental constitutive relations and the incremental Neuber’s rule. The multiaxial stress-strain state at the notch root of notched components subjected to proportional and nonproportional loading was predicted by the multiaxial approximate approach. On the basis of the multiaxial local stress-strain state and the Fatemi-Socie criterion, the fatigue lives of the notched components were predicted. The analytical results show that the proposed multiaxial local stress-strain method can describe the multiaxial stress state at the notch root very well, and the predicted fatigue lives correlate well with the experimental data.