This paper describes a device that makes it possible to carry out two-sided processing of plane-parallel plates of low rigidity. A formula is obtained for calculating the sliding velocity at an arbitrary point of a blank relative to the tool during processing on the given device. A mathematical model is developed, and the regularities with which the paths of friction are distributed in a diametrical cross section of the workpiece are numerically studied. Specific values are proposed for the geometrical and kinematic adjustment parameters of the device to ensure the required accuracy of the processed surface for various starting shapes. (C) 1996 The Optical Society of America.