Suction caisson foundations can be used to anchor tension leg platforms. The soil at the bottom of the caisson undergoes both unloading and cyclic loading under wind and wave loads. However, the problem of cyclic cumulative deformation of soft clay under unloading has rarely been addressed. So, the strain cumulative deformation and strain softening characteristics of soft clay are studied by cyclic triaxial tests. The test results show that under low static deviator stress ratios and dynamic deviator stress ratios, the soil has a low level of strain accumulation and softening. As the dynamic deviator stress ratios increase, the cumulative cyclic deformation gradually increases, which rapidly develops in the early stage and tends to stabilize in the later stage. Moreover, the softening index gradually increases and is linearly related to the logarithm of the number of cycles. The cyclic cumulative deformation of the soil increases with increases in unloading stress and dynamic deviator stress, showing a creep characteristic of attenuation and then stabilization. Based on the tests, an equivalent cyclic creep model is established to describe the strain accumulation and softening of soil and verified through comparison with the test results. Then, the model is extended to a three-dimension model, and a finite element subroutine is developed for studying the strain cumulative deformation and strain softening characteristics of soft clay.