A wire saw slicing apparatus is capable of slicing a workpiece into wafers having a flat shape free from undulations (waviness) and includes a feeding device for feeding the workpiece or a wire along a linear feed path to force them together, and a reciprocating device for reciprocating the wire in the axial direction. A program setter sets a first cyclic pattern of the feed speed of the workpiece or the wire and a second cyclic pattern of the reciprocating speed of the wire in such a relation that the first and second cyclic patterns are synchronized at least during a time period of one of the modes of the respective cyclic patterns.