Abstract: In order to simulate undrained stress-strain responses of saturated soft clays with cyclic loading, an equation elastoplastic bounding surface model is developed using the bounding surface equation which is expressed based on the Mises yield criterion, and the hardening modulus field which is described in the deviatoric stress space using methods of the hardening modulus interpolation and the mapping center movement. An incremental function of the elastoplastic modulus is established based on the radial mapping rule and the mapping center moves with the variation of loading and unloading paths for the model. Because the elastoplastic modulus interpllation function and the mapping center movement rule are used in the model, the evolution of the hardening modulus field is simple and remembered parameters are less during tracing the cyclic stress path. In addition, a parameter describing the accumulation rate and the level of shear strain is used in the elastoplastic modulus interpolation function to control the accumulation of shear strain with the number of stress cycles. The model can not only describe the nonlinear and hysteretic stress-strain responses and strain accumulation of soft clays subjected to cyclic loads but also predict the stress-strain response of soil elements with different combinations of initial and cyclic stresses. The Method determining the model parameters is also researched using the cyclic triaxial compression tests. Finally, the cyclic triaxial tensile test results are predicted using determined parameters and the rationality of the model is verified by comparing predicted results with test results.