This circular rolling mill (1), used for shaping annular workpieces (100), comprises a pair of rollers, an inner one (12) and an outer one (10), capable of working (F1+F2) the radial inner (102) and outer (101) faces of a workpiece, and a pair of conical rollers, an upper one (22) and a lower one (20), capable of working (F4+F5) the front faces (103, 104) of the workpiece, and also means (66) for moving some of these rollers (22) with respect to a frame (41) of the rolling mill (1). The means for moving at least one of the rollers (22) comprise at least one pinion (54, 55) and at least one rack (26, 28) which is secured to a member for the movement (F3) of the roller. This pinion (54, 55) is rotated by the output shaft of an electrically operated geared motor (66) mounted on a support (72) which is articulated with respect to the frame about the axis (X56) parallel to the axis of rotation of the pinion. Damping means (76) are provided for damping the pivoting movement of the support (72) about its articular axis (X56).