Several different physics mechanisms yield in enhanced oil recovery with low salinity water flooding: reduction in interfacial tension, alteration of wettability, mobilization and size exclusion of fines. In this paper the laboratory study of fines migration and straining during low salinity waterflooding is performed. First, single-phase flood with piece-wise salinity decreasing was carried out to assure the presence of movable fines in the rocks under investigation. The, sequential waterflooding by formation water, restoration of the connate water with oil and waterflooding by fresh water, were undertaken. The laboratory tests have been performed under the conditions of large scale approximation, so Welge-JBN methods for determining relative phase permeability were applicable. The relative permeability curves were obtained from the coreflood data. The obtained curves show that the permeability for water increases at low water saturations while it decreases at high saturations. The non-monotonic behavior of relative permeability for water is the main finding of this paper.