In order to further investigate the consolidation mechanism of saturated soft clay ground with sand drains, Hansbo’s flow equation was adopted to describe the nonlinear relation between flow velocity and hydraulic gradient, and the unified hardening (UH) constitutive model considering time effect was introduced to describe the elasto-viscoplastic deformation of soil. The consolidation equation of ideal sand-drained ground was modified, the discrete scheme of implicit finite difference method was given, and the corresponding Fortran program was designed. By comparing the numerical solution with the existing analytical solution of nonlinear consolidation of sand-drained ground, the effectiveness of the proposed method was verified. Then, the influences of the parameters of UH model and Hansbo’s flow on the elasto-viscoplastic consolidation process of ground with sand drains were discussed. Numerical results show that the coupling mechanism of primary and secondary consolidation was the main reason for the increase of excess pore water pressure at the early stage of consolidation. The viscosity of soil and the non-Darcy characteristics of flow both delayed the overall dissipation of pore water pressure in the sand-drained ground at the middle-late stage of consolidation. In addition, the consolidation process was accelerated with the increase of the permeability index at the later stage of consolidation.