A dust layer, especially based on high-resistivity dust, at the collecting electrodes may cause a back corona discharge in electrostatic precipitators (ESP). It can significantly reduce the ESP efficiency and as a result cause ecological damages. To study the dust layer influence inside ESPs, it is necessary to derive an adequate model of the ESP precipitation process with a dust layer at the collecting electrode. The research of the present thesis is focused on stationary studies of the precipitation process with a dust layer at the collecting electrode in ESPs. Three mathematical models are proposed as a description of the precipitation process with a dust layer at the collecting electrode. The models are based on Maxwell’s equations and the finite element method (FEM). COMSOL Multiphysics software is used for their implementation. In all models the dust layer has constant conductivity and the air region has constant ion mobility. In the first model there are no coupling conditions, which is required in mathematics, are given between the two regions. The solution found by COMSOL Multiphysics does not provide physically acceptable coupling conditions. In the second model, a continuous transition zone is introduced between the two regions so that no coupling conditions are required. With the large derivatives in the transition zone, the nonlinear solver in COMSOL Multiphysics does not converge. Finally, in the third model, the dust layer and the grounded collecting electrode are replaced with a boundary condition for the air region. The properties of the third model are investigated, and these models can be used to study the influence of the dust layer. The results of these investigations are reported and discussed.