Abstract. At present time there is not information about the influence of rigidity of hardened steel parts on the parameters of flatness deviations: EFEmax, EFEa, EFEq, which are called correspondingly greatest, arithmetic average and quadratic average. To model the variable rigidity of workpieces, an arrangement with the frame structure was used. It allowed to simulate the variable compliance of parts with constant sizes in the direction of longitudinal feed of grinding machine. Searching for models of multiple dispersion analysis was carried out using the D-optimal plan of experiment. They predicted that in rough grinding all parameters of flatness deviations increase with the growth of the part rigidity. In the subsequent grinding stages, the increase of part rigidity is accompanied by the favorable decrease of the flatness deviations. The compliance of low-rigid parts in the finishing stage of grinding should be reduced using additional technological devices.