A grinding machine includes a pair of workpiece support devices (12, 13), which clamp and rotate a workpiece (W), on a bed (11). A pair of saddles (14) is provided on the bed (11) in such a way as to be movable along the rotational axis of the workpiece (W). Grindstone heads (16) provided with rotating grindstones (16c) and drive mechanisms (16d) are supported on the saddles (14) in such a way as to be movable in a direction that perpendicularly intersects the movement direction of the saddles (14). There is provided a partition structure (20) which consists of a fixed cover (21) and a extendable cover (22), and serves to partition a machining region (T) for the purpose of sealing off the same so that the clamping portions (12a, 13a) and the rotating grindstones (16c) of both of the workpiece support devices (12, 13) will be located inside the machining region (T), and that bearing sections (12b, 13b) and driving sections (12c, 13c) of both of the workpiece support devices (12, 13), as well as bearing sections (16b) and driving sections (16d) of both of the grindstone heads (16), will be located outside the machining region (T).