The local cyclic elastic-plastic stress-strain responses were simulated using the incremental plasticity procedures of ABAQUS finite element code. It is shown a better understanding on the evolutions of the local cyclic stress-strain and the strong interactions between the most stressed material element and its neighboring material elements in the plastic deformations and stress redistributions. Based on the stress/strain states of the stabilized cycle, a new damage parameter, proposed on modification of the ASME code parameter, is applied and improved correlations between the predicted and the experimental fatigue lives are shown. It is concluded that the improvement of fatigue life prediction depends not only on the fatigue damage models, but also on the accurate evaluations of the cyclic elasto-plastic stress/strain responses.