On the bases of the assumption that certain materials can be typed as visco elastic-plastic bodies, a constitutive equation for the stress-strain response of such materials was derived. Then, the correlation was investigated between fatigue limit and the stress at the transition point, the point where the deformation mechanism of the material changed from visco elastic into visco elastic-plastic behavior. Complete compression-to-tension load-controlled axial constant amplitude loading test progmam was performed for mild steel plane specimens. As a result, following two main points are obtained. 1) The constitutive equation derived from the visco elastic-plastic model can satisfactory represent cyclic stress-strain response. 2) Both fatigue limit and the stress at the transition point were obtained, and they were found to be almost identical.