Abstract: A method of and apparatus for reducing the thickness of (or skiving) regions of sheet material workpieces, e.g. shoe upper components, involves feeding a workpiece 14 to a band knife (4) and, in advance of said knife, applying pressure to the workpiece 14, using a row of pressure-applying elements (18) to deform a region of the workpiece in relation to the cutting plane (20) of the knife. By controlling the elements (18) to operate in successive sequences of combinations, regions of the workpiece (14) are successively skived as the workpiece (14) passes the knife (4). The operation of the elements (18) is controlled by a computer (CPU), having a memory in which workpiece information data, relating to certain workpiece parameters, as well as in accordance with shape, positional and orientational data is stored. Such data may be generated using optical recognition workpiece means (100,120,140,160).