Large-deformation finite element (LDFE) analysis with the coupled Eulerian–Lagrangian (CEL) technique for large-deformation soil functions without twisting or distorting the mesh. However, the model does not consider the strain-softening and strain-rate dependence of clay-based soils. The undrained shear strength of clay is sensitive to the strain rate. In addition, the strain-softening effect of soil strength reduction accompanied by large-scale shear deformation should be considered. In this study, anchor dragging simulations were performed for large-deformation analysis considering strain-softening and strain-rate dependence. Furthermore, a shear strength equation expressing the strain-softening and strain-rate dependence of the Tresca constitutive model was developed based on VUMAT, an ABAQUS/Explicit subroutine. The equation was designed so that it could be linked to the LDFE/CEL model. The model was verified by performing comparative analysis with the Mohr–Coulomb (M–C) perfect-plasticity model. The newly constructed Tresca base strain-softening and strain-rate-dependence VUMAT algorithm in the LDFE/CEL model analysis confirmed the effects of strain-softening and strain-rate dependence. The proposed model enabled a highly realistic simulation of the actual phenomenon than the M–C model. Finally, a parametric study on strain-softening and strain-rate dependence was conducted, and the behavior of clay due to the anchor drag phenomenon was revealed.