The self-potential method can be used to detect and monitor anomalous seepages in dams and embankments. In such a case, an electrical field of electrokinetic nature (i.e., associated with pore water flow) can be measured using a set of non-polarizable electrodes typically located at the ground surface or in some wells. This field can be in turn related to the pattern of groundwater flow. We built an experimental dam to investigate to which extent the self-potential method can help characterizing seepages in dams. We first use the finite element method to simulate the ground water flow in a heterogeneous porous and permeable material by solving the groundwater flow equation. The resulting groundwater flow solution is then used to compute the electrical potential distribution by solving the corresponding elliptic partial differential equation. In a preliminary experiment, we could not measure any self-potential anomaly associated with the infiltration of water in the dam. Our numerical simulations showed that the magnitudes of the self-potential anomalies were controlled by (1) the nature of the flow regime (viscous laminar versus inertial laminar flow regimes) and (2) the presence of insulating Polyvinyl Chloride (PVC) tubes located at the end of the preferential flow channels in the structure of the dam. Thanks to these numerical simulations, we added sand at the entrance of the infiltration area in order to reduce the effects of the PVC tubes and to restrain the flow regime to the viscous laminar flow regime. New experiments allowed for detecting a self-potential anomaly with an amplitude of around −9 mV consistent with that obtained through numerical modelling with a finite element simulator. This comparison was used to test the accuracy of the modelling approach and define the strengths and weaknesses of the self-potential method to determine preferential seepages in earth dam structures.