Vertical drains improve the consolidation of soft clay, characterized by the large void ratio, high compressibility, and high water content, but the consolidation theory still needs to be improved. This paper investigated the large-strain consolidation of soft clay with vertical drains under free-strain theory, considering the elastic viscoplastic constitutive relation of soft soil, the coupled vertical–radial non-Darcian flow, and the logarithmic relationship of the permeability coefficients. Meanwhile, the nonideal cylindrical unit cell of the soil was captured by taking into account the permeability of the vertical drain decreasing with time (variable well resistance) and the smear effect. The proposed model was verified by degenerating into the cases in the extant literature and applying it to two laboratory tests using the finite-difference method. The most salient finding of the parametric analysis was that the average degree of consolidation curve might show two ups and downs due to the rheological property of soft clay. Several parameters reflecting the impacts of the smear zone and well resistance were also studied. The results demonstrated that some factors related to soil permeability and boundary conditions could enhance the phenomenon of increasing pore pressure. [ABSTRACT FROM AUTHOR]