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The motion of an individual deformable erythrocyte in a capillary whose diameter is smaller than the particle diameter has been considered. The problem formulation is based on the Lighthill-Fitzgerald model. The erythrocyte drag at a given pressure difference acting on its frontal surface has been determined. The dependences of the relative drag on the dimensionless parameters of the model as well as on the minimum thickness of the lubricating layer and the rate of motion of the erythrocyte on the pressure at opposite edges of the cell have been obtained.Simulation of the blood flow in the microcirculatory system is one of the key problems arising in quantitative descriptions of the convective heat transfer and the thermoregulation and oxygenation of living biological tissues. As compared to the hemodynamic problems for arteries, this problem is more complicated, since the blood in tiny vessels can no longer be considered as a continuous medium. The main (greater in number) form elements of blood -erythrocytes -that comparable in diameter to capillaries, and they are sometimes larger than capillaries. Motion of red blood cells under such conditions turns out to be possible only due to the high deformability of their membranes and the formation between the surface of these cells and the capillary wall of a thin plasma layer acting as a lubricant.The biomechanical properties of blood particles and vascular walls, as well as the blood flow in tiny vessels, have been the subject of many papers, including [1][2][3][4][5][6]. In [2], it was shown that in the gap between two erythrocytes moving through a capillary (the so-called "bolus") plasma should circulate in the direction of the particle motion on the axis and in the reverse direction by the wall. In [4], the deformation of erythrocytes in capillaries depending on the vessel diameter and the rate of motion of particles was investigated experimentally. The ratios were obtained and the velocity profile of plasma in the bolus was calculated. In [5], the motion of erythrocytes through capillaries with diameters close to critical ones was investigated. The size of the latter depends on the geometric and mechanical properties of the red blood cells: they deform at a constant volume (the liquid inside erythrocytes is incompressible) and an almost constant area of the surface (the erythrocytic membrane is poorly stretchable). In [6], the motion of a suspension of elastic incompressible spheres through a capillary was considered. The development of this model was motivated by the interest in investigating the motion of leukocytes (white blood cells) through the microcirculatory system.One of the earliest physicomathematical models of blood flow in narrow capillaries is the Lighthill model [7] constructed in the approximations of lubrication theory. The local elastic properties of the vessel wall and the erythrocyte in the first approximation in [7] were assumed to be proportional to the excess pressure. The equation of motion was reduced to the Reynolds equation for the lu...

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