Aiming at the stability of storage facilities built in soft soil areas, this paper analyzes the influence of cyclic loading on consolidation during used stage. Firstly, the nonlinear compressibility and permeability of soil are introduced, the well resistance and three kinds of radial permeability coefficient modes are considered, the corresponding governing equations are obtained, and the corresponding analytical solution is obtained by the separate variables method. Then, the corresponding solution under the action of trapezoidal and triangular cyclic loading is obtained. The rationality of the solution in this paper is verified by the degradation method. Finally, the settlement of storage facilities during the using period is predicted by case analysis. The results show that the ratio of soil compression index to permeability index (Cc/Ck) and the radial permeability coefficient mode have no significant influence on the average consolidation degree. The load-related intermittent parameter β, the loading parameter α, and the parameter Nσ have a great influence on the average consolidation degree. The smaller the three parameters are, the more energy the load generates at the same time, and the greater the corresponding average degree of consolidation. The solution can be effectively applied to nonlinear radial consolidation analysis under trapezoidal and triangular cyclic loadings.