The elution of high-viscosity substances from a granular bed using fluids with different interfacial tensions was investigated. Analyses of changes in flow resistance and the degree of saturation of the deposit during the process were conducted. The elution process was described by means of the modified concept of capillary bundles, based on the Blake-Kozeny-Carman relationship. The use of this dependence can be helpful in determining the degree of saturation of the deposit at any given time of elution process only on the basis of the flow hydrodynamics and parameters of the deposit and liquid. This makes it possible to estimate the residual saturation of the bed without the need to perform troublesome experimental research for the content of oil in the reservoir.