Three-dimensional problems of consolidation with vertical drains are sometimes simplified as plane-strain ones to facilitate the operation of numerical analyses. It requires establishing an equivalent relationship between the three-dimensional consolidation with a vertical drain and the two-dimensional consolidation with a sand-wall drain. Analytical solutions for two-dimensional consolidation with a sand-wall drain are, therefore, the important basis for determining the equivalent consolidation parameters. To analyze the applicability of the existing approximate solutions of equal-strain consolidation with a sand-wall drain, an analytical solution for free-strain consolidation is derived based on the rigorous governing equations for soil element volume. An important effect of drain resistance on consolidation is considered. A general drainage boundary condition is taken into consideration, including fully drained condition and impeded drainage condition. Comparisons are made between the existing solutions and the proposed solution. In addition, the effects of Poisson’s ratio, vertical and horizontal drainage on consolidation are investigated. It is shown that the existing solutions for consolidation with a sand-wall drain are approximate but sufficiently accurate. The consolidation is mainly governed by horizontal consolidation. Vertical consolidation is however negligible. Consolidation rate increases with the increase of Poisson’s ratio. This factor should be considered when a sand-wall drain is equivalent to a vertical drain.