A double disc surface grinding machine includes a clamp band which has a non-circular outer circumferential portion. The clamp band is attached to an outer circumferential surface of a work and is housed, under the attached state, in a storage portion which has a non-circular inner circumferential portion engageable with the outer circumferential portion of the clamp band, movably in a first direction. A rotation drive unit rotates the storage portion around a first rotation shaft extending in the first direction, to make the inner circumferential portion of the storage portion engage with the outer circumferential portion of the clamp band, thereby rotates the clamp band and the work together with the storage portion. At least one of the grinding wheels is fed onto the work so as to sandwich the work with a pair of rotating grinding wheels for grinding two main surfaces of the work.