A suction anchor is an appealing anchoring solution for floating production. However, the possible effects of residual pore pressure can be rarely found any report so far in term of the research and design. In this study, the residual pore pressure distribution characteristics around the suction anchor subjected to vertical cyclic loads are investigated in a soft clay seabed, and a three-dimensional damage-dependent bounding surface model is also proposed. This model adopts the combined isotropic-kinematic hardening rule to achieve isotropic hardening and kinematic hardening of the boundary surface. The proposed model is validated against triaxial tests on anisotropically consolidated saturated clays and normally consolidated saturated clays. The analytical results show that the excess pore water pressure accumulates primarily on the outside of the suction anchor, whereas negative pore water pressure mainly on the inside. The maximum values of both sides appear in the lower part of the seabed. According to the distribution characteristics of the residual pore pressure, a perforated anchor is proposed to reduce the accumulation of excess pore water pressure. A comparative study generally shows that the perforated anchor can effectively reduce the accumulation of excess pore water pressure.