Catalytic hydrogenation of the plant oils includes a filtration stage in which the solid catalyst must be separated from its suspension in the melted hydrogenation products. For effective separation of the catalyst, a proper selection of the filter cloth and filtration conditions is necessary. The subject of this study is filtration of finely dispersed carbon material Sibunit through a porous woven filtering cloth in circulation mode. Sibunit is the carrier for Pd catalysts that are regarded as prospective for hydrogenation of vegetable oils; the carbon-based catalysts can be reused and can therefore be more economical than conventional nickel catalysts. To reliably predict the efficiency and duration of filtration of the catalyst suspended in the hydrogenated products, the mathematical model of the filtration process must adequately describe the complex physical phenomena that occur during the process. In the article, a one-dimensional mathematical model was developed, which took into account the main physical phenomena of the filtration process, such as percolation of the particles through a porous filter, accumulation of the particles along the filter pores, and a gradual cake growth. Woven fabric contains two types of pores: the pores between the threads and the pores between the fibers. Model assumes that polydisperse particles can both penetrate through the filter cloth and accumulate inside the tissue and on its outer surface. It is assumed that the hydraulic resistance of the cake increases due to the growth of its height only, and the hydraulic resistance of the filter cloth increases due to particles trapped in the pores. Numerical analysis of the model was carried out in the range of parameters typical for industrial conditions. It has been found that the process efficiency, which was defined as the minimum time required filtering a certain amount of hydrogenated oil to the maximum degree of catalyst purification, depends mainly on the time taken to form a cake layer of sufficient height. Higher efficiency of the filtration process is favored by the higher filter porosity, the greater thread diameter, and the smaller pore size between the fibers. In contrast to the thin pores formed by the fibers, the large pores between threads allow more particles to pass through the filter; therefore, for practical use it is necessary to adjust the filter cloth porous structure with the particles size distribution. The model was verified by comparing the predicted results with experimental data.