The reliability of a connector depends on the contact force generated by the spring in the terminal of a connector. The springs are commonly formed by stamping from a strip of spring material. Therefore, the prediction of the force — displacement relation by the finite element (FE) method is very important for the design of terminals. For simulation, an accurate model of stress-strain (s-s) responses of the materials is required. When the materials are deformed in the forward and then the reverse directions, almost all spring materials show different s-s responses between the two directions, due to the Bauschinger effect. This phenomenon makes simulation difficult because the s-s response depends on the prior deformation of the material. Hence, the measurement of the s-s response is the elementary process, by cyclic tension and compression testing in which materials deform elastically and plastically. Then, the s-s responses should be described accurately by mathematical models for FE simulation. In this paper, the authors compare the experimental s-s responses of copper-based materials with conventional mathematical models and the Yoshida-Uemori model, which is a constitutive model having high capability of describing the elastic and plastic behavior of cyclic deformation. The calculated s-s responses only by Yoshida-Uemori model were in very good agreement with the corresponding experimental results. Therefore, the use of this model for FE simulation would be recommended for a more accurate prediction of force-displacement relation of the spring.