Abstract: Based on a four-element rheological model, the one-dimensional rheological consolidation problem of soil under one-step loading was studied by introducing continuous drainage boundary conditions. The analytical solution under constant loading is obtained by the separation variable method and the Laplace transform technique, and the analytical solution under one-step loading is obtained by the integral method. Then, by degrading the drainage boundary and rheological model, the solution of one-dimensional rheological consolidation under the Terzaghi's boundary and the three-element rheological model is obtained, and the correctness of the present solution is verified by the comparison with existing solutions. Finally, the consolidation behavior of soil is analyzed for different interface parameters, rheological parameters or loading rate. The results show that:the difference between the consolidation solution based on continuous drainage boundary conditions and that based on Terzaghi's drainage is mainly in the early stage of consolidation, and the difference decreases with the increase of interface parameters α and β. The difference between rheological consolidation and linear elastic consolidation is mainly in the late stage of consolidation, and rheological consolidation requires a longer time for soil to be fully consolidated. In addition, the consolidation rate of soil increases with the increase of loading rate.