The scaled boundary finite-element method, a semi-analytical computational scheme primarily developed for dynamic stiffness of unbounded domains, is applied to the analysis of unsteady seepage flow problems. This method is based on the finite-element technology and gains the advantages of the boundary element method as well. Only boundary of the domain is discretized, no fundamental solution is required and singularity problems can be modeled rigorously. Anisotropic and non-homogeneous materials satisfying similarity are modeled with no additional efforts. In this study, firstly, formulation of the method for the transient seepage flow problems is derived followed by its solution procedures. The accuracy, simplicity and applicability of the method are demonstrated via four numerical examples of transient seepage flow – three of them are available in the literature. Homogenous, non-homogenous, isotropic and anisotropic material properties are considered to show the versatility of the technique. Excellent agreement with the finite-element method is observed. The method out-performs the finite-element method in modeling singularity points. Copyright © 2014 John Wiley & Sons, Ltd.