Based on the theories of bounding surface and multiple surface, a three-surface cyclic constitutive model, which is applicable for engineering because of the simple form and less parameters, was established to describe metal material behavior under the triaxial cyclic loadings. The plastic strain was decomposed into plastic strain 1 corresponding to a bounding surface model and plastic strain 2 corresponding to a single yield surface model. An evolution formula of the distance between the current stress and the image stress on the bounding surface was developed, which makes the plastic modulus calculation be coupled with the kinematic hardening rule through the consistency condition of the yield surface. As the hardening parameter, the plastic strain was calculated according to the associated flow rule. Compared with the classic bounding surface models, it has a concise form, and compared with the modified kinematic hardening rule models, it has less parameters. The existing experimental results about stable metal material U71Mn under uniaxial cyclic loading were adopted, and four mechanical behaviors were considered. The ratcheting were simulated by the model considering the effect of mean stress and stress amplitude under asymmetrical stress cycling, and the maximum strain amplitude memory effect was analyzed under symmetrical strain cycling. The calculated results agree well with the experimental results, which means the proposed model provides a new method to study the constitutive relation.