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.