Analyzing instability in geomaterials in the form of shear localization using finite element discretization leads to erroneous results if the constitutive formulation does not contain any internal length scale. Thus, the solution becomes mesh dependent. The remedy of such problem is commonly known as regularization. Use of coupled solid–fluid formulation for the modeling of saturated porous media is one the remedial measures or regularizations schemes. The present study explores the efficacy of this regularization scheme by modeling the deformation in stone columns. Stone column is a ground improvement technique to accelerate consolidation settlement in low permeable soils. During consolidation, stone column also undergoes axial deformation along with the surrounding soil. The deformation mode in stone column is either punching or bulging or shear failure depending on the rate of loading and boundary conditions. Earlier studies indicate shear deformation in stone column is often associated with complex localized bands, which cannot be captured through the conventional analytical solutions. The present analysis using finite elements demonstrates that with mesh refinement the thickness of shear band within the stone column reduces despite using such coupled formulation. However, the overall time settlement profile of the column is unaffected by localization. In addition, the results are found to be affected by the selected time increment as the total consolidation time varies with the step time variation. The regularization scheme seems partially successful to model the localized deformation in stone columns.