Machine (10) for grinding thin-walled workpieces (40), in particular by means of shoe grinding, with a clamping device (50) which has a chuck (54) rotatable about a longitudinal axis (52) and which has a contact surface (56) for a thin-walled, ring-like Workpiece (40), - a support unit (60) with at least one support shoe (62, 64) to support the workpiece (40) in a position eccentric to the longitudinal axis (52), and - at least one grinding spindle (18) which can accommodate a grinding tool (80, 84) for processing the workpiece (40), characterized in that the contact surface (56) has at least one recess (110) which can be coupled to a suction unit (140) for generating a suction force, and that the workpiece (40) is held eccentrically on the chuck (54) due to the suction force.
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