<p>Seepage is an important engineering event that causes material and moral damages that are difficult to prevent in hydraulic structures. In this paper, the two-dimensional transient seepage analysis of the concrete dam's foundation is examined using the finite element method (FEM) in the Laplace domain for the first time. The effects of homogeneous and inhomogeneous soil types, different geometric properties, and the presence of a cut-off wall on the seepage are examined in detail. To solve the partial differential equation obtained in line with Darcy's law and continuity equations, the FEM based on the Galerkin method in the Laplace domain is applied. The results are transformed to the time domain using the modified Durbin's numerical inverse Laplace transform. A program coded in Fortran is used to conduct various seepage analyses. It is observed that the seepage phenomenon occurring at different points and times can be determined easily and effectively. The consistency of the hydraulic head values obtained for transient seepage cases with the literature results reveals the accuracy, applicability and effectiveness of the proposed method.</p>