A multiplicity of wafers are sliced from a workpiece which has a longitudinal axis and a cross section, the workpiece fastened on a table being fed by a relative movement directed perpendicularly to the longitudinal axis of the workpiece between the table and the wire gang of a wire saw, with a variable forward feed rate through the wire gang formed by a sawing wire moved with an effective speed, the effective speed of the sawing wire being regulated as a function of the forward feed rate and the workpiece cross section so as to result in uniform wear of the sawing wire.