An analytical solution to the problem of two-dimensional steady-state seepage flow beneath a water-retaining structure is presented using conformal mapping and complex variables. This paper addresses the question of to what extent the cut-off thickness affects the values of seepage characteristics. The closed-form analytical equations are calculated numerically. The analytical results have been validated by comparing them with the available exact solutions for finite-depth seepage. The resulting implicit equations, involving elliptic integrals, are used to create design diagrams. Increasing the thickness can cause a reduction in hydraulic gradient, seepage discharge, and uplift pressure at the left tip of the cut-off. A customized fragment type considering the cut-off’s thickness is developed using the analytical results to estimate seepage quantities and exit gradients. The form factor for this fragment is obtained in the form of dimensionless charts, which predict the flow rate and exit gradient more precisely than the existing solutions.