Numerical modeling of the problem of dam monitoring by the Electrical Resistivity Tomography method is carried out. The mathematical model is based on integral equations with a partial Fourier transform with respect to one spatial variable. It is assumed that the measurement line is located across the dam longitude. To approximate the shape of the dam surface, the Radial Basic Functions method is applied. The influence of locations of the water-dam, dam-basement, basement-leakage boundaries with respect to the sounding installation, which is partially placed under the headwater, is studied. Numerical modeling is carried out for the following varied parameters: 1) water level at the headwater; 2) the height of the leak; 3) the depth of the leak; 4) position of the supply electrode; 5) water level and leaks positions are changing simultaneously. Modeling results are presented in the form of apparent resistivity curves, as it is customary in geophysical practice.