The article considers the methodology for calculating the design parameters of the functional surfaces of the steady-rests, which determine the accuracy and productivity of surface treatment of blanks. A mathematical model for calculat-ing the quality parameters of the functional surfaces of fixed steady-rests is presented. This model is built on the basis of the guaranteed result method and assumes: the inner and outer cylindrical surfaces of self-centering lunette rollers are elliptical and misaligned axes; Contact of the rollers with the workpiece is elastic; The rollers are pre-pressed to the elliptical surface of the workpiece with forces ensuring constant contact between the rollers and the workpiece; The rollers rotate at a constant angular velocity.