The flow of pore fluid is modeled on a lab scale with samples of man-made substance from tailings ponds. The data obtained in the gravimetric and apparent resistance tests are presented. It is found that capillary forces make the main contribution to flow of solutions from a pollution source. This allowed estimation of nature and velocity of the process. The experimental results show high-rate vertical and lateral spreading of solid waste substance from sources of drainage solutions, which has detrimental effect on ecology of the nearby lands and water bodies.