A handheld oscillation machine tool has support devices for maintaining a spacing between internal parts and an outer housing. The support devices are arranged in pairs of first and second support devices. One support device in each pair has a concave circular surface, and the other has an opposed convex circular surface. Elastically deformable damping elements are arranged between the pairs of support devices. The damping elements are deformed from original flat conditions under forces applied by the support devices, and have concave and convex circular surface adjoining the opposed concave and convex circular surfaces at the support devices.