Disclosed are a method and a machine for profiling the narrow lateral faces of plate-shaped workpieces (2), said faces being disposed opposite each other and running parallel to each other. The profiling process takes place across a profiling zone located within the flat passage of a slideway (1), in which cutting profiling tools (6) are arranged laterally next to the slideway. The workpieces are advanced via a top force device (3, 4) which rolls off the top faces thereof. In order to make the profiled narrow lateral faces run parallel with high accuracy, a straight guiding groove that extends in the direction of advancement is cut into the workpieces. A straightening device (11), upon which the workpieces comprising the directing groove are received and guided, is disposed at least across the profiling zone within the region of the slideway of the machine.