The study is devoted to the analytical description of the residual moisture of leather (semi-finished leather product after dyeing) taking into account the deformation and filtration properties of the semi-finished leather product at this stage. Mathematical models of changes in the removed fluid, hydraulic pressure in the area of leather squeezing, and residual moisture content are determined. The study of the squeezing process based on these models makes it possible to determine with sufficient accuracy the appropriate parameters for roller squeezing of leather, necessary for the rational design and operation of squeezing machines. A condition was established for obtaining minimum residual moisture during roller squeezing, which allows for an increase in the efficiency of roller squeezing of leather.