A mathematical model of the motion of 3-dimensional erythrocytes along fragments of capillary networks consisting of a small number of narrow capillaries is constructed. The model takes into account the lengths and inner diameters of capillaries , the form and position of an erythrocyte in a capillary, the viscosity of the plasm and the contents of an erythrocyte, the volume and surface area of an erythrocyte, the elastic characteristics of an erythr ocyte, the membrane rolling of an erythrocyte, and the intervals between the entries of erythrocytes into t he capillary network. The formulas for the dependence of pressure differential causing the blood flow i n fragments of capillary networks on the parameters of the model are obtained. The dependences of the blood flow rate through a capillary tee on the lengths of capillaries forming the tee, on the pressur e differential at the ends of the tee, and on the intervals between the entries of erythrocytes into the t ee are obtained. Experimental and theoretical studies of hemodynamics in a microcirculation system allows us to describe quantitatively the interrelated moti on of the viscous plasm and elastic cells (erythrocytes) along capillaries. In ord er to describe the motion of the plasm, we may use the basic hydrodynamic equations (equations of motion and continuity), and the form of erythrocytes is characteri zed by equations of the mechanics of a deformed solid body. The simultaneous solution of those equations subject to the corresponding boundary conditions determines the spatial distribution of the pressure in the plasm, the velocity of the plasm and erythrocytes, and the energy consumption for the blood motion in capillaries. The existing models using these relations simulate the complicated character of inte raction of blood cells in microvessels only in the first approximation (2, 4, 5, 7-12, 1 5, 16, 19, 21, 25, 26). Thus, the rheological properties of blood were considered in (26), the erythrocyte membrane rolling in wide capillaries (with the diameter exceeding the diameter of the erythrocyte) was considered in (16). An asymmetric form of an erythrocyte in a wide vessel was considered in (8), the motion of an erythrocyte having a symmetric parachute shape was considered in (15), in papers (4, 12) erythrocytes had the shape of elastic balls and in (5) were shaped as cylinders. A 2-dimensional model with a rolling membrane was constructed in (19). However, such important characteristics as the volume and surface area of erythrocytes were not taken into account in those models. The amount of oxygen transported by an erythrocyte depends on its volume and the rate of oxygen release from an erythrocyte is determined by its surface area. A three-dimensional model of the motion of an erythrocyte along a capillary was