The features of the final machining of thin-walled plates are given. The calculation scheme for the kinematic parameters of abrasive finishing of thin-walled easily deformable plates and the mathematical dependence for calculating the pressure on the lapping faceplates with the processed parts are determined. The aim of the work is to obtain an analytical dependence that establishes the relationship between the operating parameters and the conditions of the abrasive finishing process with the roughness of the working surface of the plates. The task, which the article is devoted to solve is theoretical and experimental studies of the influence of technological modes and conditions of abrasive finishing of plates with complex relative movement of parts and lapping on the roughness of the treated surfaces, as well as in the development of a methodology for determining rational modes and conditions of surface treatment of thin-walled plates. Theoretical research was carried out on the basis of the main provisions of mechanical engineering technology, grinding theory, theoretical mechanics, theory of elasticity and plasticity, probability theory and mathematical statistics. Experimental studies have been carried out according to standard methods in production and laboratory conditions using certified control and measuring equipment. The obtained data were processed using computer technology and presented in the form of empirical dependencies that are convenient for practical application. The originality of the work consists in obtaining mathematical dependencies for calculating the kinematic parameters and parameters of the contact interaction of abrasive particles with the treated surfaces of the plates, which allow determining the rational values of the ratio of the speeds of movement of the plates and lapping.