The work uses the micropolar theory of the continuum, in which the asymmetric stress tensor is used to describe the stress state. The theory is applied to the case of suspension movement in a thin layer between approximately parallel surfaces and with curvature radii large enough compared to the average layer thickness 6. Obtained approximate differential equations of motion of the lubricating layer of suspensions, as well as approximate equations for the distribution of the concentration of a thin layer of suspension. Then the resulting system of differential equations is solved, and the integral terms are not taken into account.