The invention relates to a machine (10) for processing in particular plastic spectacle lenses (L), comprising a machine housing (18) which surrounds a working chamber (24) located between a workpiece spindle (26) for rotationally driving the spectacle lens about a workpiece axis of rotation (B axis) and a fast tool servo (28) for producing an oscillating feeding movement (F axis) of a rotary tool (30) in the direction of the spectacle lenses. The workpiece spindle is provided with a carriage (32) which can be driven and is guided on at least two guide surfaces (34, 36) of a guiding arrangement (38) in order to produce a relative advancing movement (X axis) between the spectacle lens and the rotary tool, said advancing movement running transversely with respect to the feeding movement and defining therewith a processing plane (F-X plane) in which during processing the rotary tool engages with the spectacle lens. For a very compact and rigid configuration of the machine, the guiding arrangement is mounted on the machine housing such that the processing plane extends between the two guide surfaces.