The present invention relates particularly to an oscillating grinding machine. The grinding machine comprises a driving motor (3) surrounded by a body (3), and a drive shaft (4) cooperating with the driving motor. The drive shaft comprises a grinding head (5) that constitutes a support for a grinding product (8). The drive shaft (4) is arranged in two pieces and comprises a main shaft (11) and an eccentric shaft (10) arranged rigidly thereto. The eccentric shaft comprises a center line (12) that assumes an angle (α) against a corresponding center line (13) of the main shaft, and thus the grinding head (5) will assume an eccentric placement in relation to the main shaft (11). Thus, the grinding head is arranged to oscillate in a substantially spherical plane provided by the rotation of the main shaft and the eccentricity and inclination of the eccentric shaft in relation to the main shaft.