Abstract: Cylindrical surface regions (1) of cutting tools (2, 21), such as drills, boring tools, reamers or the like, that is, cutting tools formed with chip removal grooves or flutes or recesses (6), are ground by engaging a rotary cutting disk (3) against the ribs (5) between the chip removal grooves. The cutting tool (2, 21), during the grinding operation, is rocked or oscillated to-and-fro (24) about its longitudinal axis (18) in such a manner that the cutting disk (3) covers the cylindrical surface portion in circumferential direction at least several times. The cutting disk (3) also may rock or oscillate about an axis perpendicular to the axis (7) of rotation of the cutting disk (3). Suitable frequencies are between about 0.1 Hz and 1 Hz, preferably 0.5 Hz, for the rocking movement of the cutting tool (2, 21), with the oscillatory movement of the grinding disk being higher than that of the cutting tool, and for example between 1 Hz and 10 Hz.