Abstract: A machine for grinding of toric surfaces on optic lenses. A holder is provided for a lens (L.sub.1) and is pivotally supported in a carriage of a compound support of two carriages. A swivel arm is secured to a pivot of a holder. The swivel arm is pivotal about a movable bearing. A holder for a grinding spindle with cup tool thereon is supported on the machine frame by means of a bearing ring. During a movement of the compound carriage, the workpiece holder moves due to the guiding of the swivel arm on a circular path, the radius of which determines the base curve of the torus surface. By supporting the weight of the holder through a compound support on the machine frame, bending stresses of the swivel arm are avoided, through which a high precision machining operation is achieved.