Lapping of plane surfaces is the technology which allows achieving high surface quality. Kinematics of lapping has the main effect on the flatness of active plane of the lapping tools as well as on the quality and flatness of the machined surface. Lapping machines can be used for grinding without the chuck-related problems as encountered in conventional surface grinding. The configuration of a conventional single-disk lapping machine was modified and the rotational velocity of a workpiece holder can be precisely controlled by a stepper motor. Two types of tools were used for experiments on a modified machine. The first tool was equipped with grinding inserts made of resin and synthetic diamond micrograins (grit size 3/2 m). In the second stage of experiments the single-layer electroplated diamond tool (D107 – grit size 106/90 m) was applied. Ceramic workpieces (Al2O3) were machined on the modified single-disc lapping machine with the use of both tools and with additional loose abrasive. Experimental results of removal rates, technological parameters and kinematical analysis are the subject of the presented paper.