Modeling of the processes of elution from porous systems is essential importance for development of the removing oily contaminations from the soils and intensification of the oil recovery processes. In the paper, capillary model of gravitational elution of high viscosity substances from the porous medium by using low viscosity liquids was derived. This model allowed for the prediction of changes in time of such parameters like: level of bed saturation with oil, relative bed permeability, liquid flow rate, flow resistance, volume of eluted liquid during the process. When modeling, phenomena and the physical properties associated with the analyzed process, such as, for example, the effects of surface tension, fluids viscosity, specific size of the granular bed, initial oil saturation of bed, variable process driving force, and the flow of liquid through the preferential flow paths, were taken into account. This allowed for the more complete imaging of elution process. The model has been verified on the basis of the results of experimental studies. In addition, the discussion on the behavior of the model due to changes in values of various parameters was carried out.