The analysis of the stability of retaining walls requires determining the stress distribution behind the wall. The stability analysis becomes significant when dealing with groundwater flow because seepage flow behind the retaining wall can reduce the resisting forces and consequently decrease the wall's stability. This issue becomes more prominent when the wall is used for drainage purposes, as the hydrostatic water pressure no longer exists, and the water pressure needs to be calculated separately from the seepage analysis or concurrently with the effective stress using existing relationships. In this study, the stress characteristic method was employed to analyze a retaining wall equipped with a vertical drain in two general conditions: plane strain and axisymmetric states under both active and passive conditions. The study considered isotropic and non-isotropic soil conditions. Additionally, the differential quadrature method was used to analyze the seepage flow. To accomplish this, a computer program was developed using MATLAB, and the obtained results were validated using the results of other research studies, finite element models simulated by PLAXIS 2D software, and finite elements limit analysis using the OPTUM G2 program. To investigate the effect of seepage on the lateral earth pressure coefficient in retaining walls with axisymmetric symmetry, a comprehensive parametric study was conducted.