Abstract: The suction anchor with taut mooring system is an important floating platform foundation in deep water. Large deformation of soil occurs under the combination of static and cyclic loadings, which impacts the stability of the suction anchor foundation severely. A pseudo-dynamic visco-elastic plastic constitutive model which describes the undrained cyclic stress-strain response of saturated soft clay is introduced. The model combines the equivalent visco-elastic theory with the creep theory, describing the nonlinearity and hysteresis of the cyclic stress-strain relationship through the equivalent visco-elastic model and the cyclic accumulative characteristic through the creep theory. Based on the pseudo-dynamic visco-elastic plastic constitutive model, a pseudo-dynamic visco-elastic plastic finite element method is developed for the assessment of the deformation process of the suction anchor foundation subjected to the combination of the static and cyclic loadings. The method does not track the cyclic stress-strain response, but treats the number of cycles as the time. The cyclic deformation of anchor foundation is determined by the equivalent visco-elastic calculation. The accumulative deformation is determined using the initial strain method on the basis of the static stress and cyclic accumulative strain potential. The relationship between the deformation and the time of anchor foundation that is the displacement-time history curve can be obtained according to the cyclic and accumulative deformations. The comparison between the calculated results by the finite element method and the anchor model test results under 1g conditions shows that the both are basically in agreement.