PURPOSE: To enhance processing accuracy and processing efficiency by supplying an adequate amount of processing liquid to the part to be cut by pressing the material to be processed against a wire from its upward to downward direction, and preventing scratches or cracks developing on the processed surface of the material to be processed with the wire when the wire is pulled out on completion of the processing.

CONSTITUTION: During the process of a wire 1 running in the direction of transfer under making reciprocal and linear movement, a material to be processed 3 is pressed against the wire 1 from its upward to downward direction. As a result, a wedge-shaped space 10 is formed between the wire 1 and the material to be processed 3 on the downstream side of the running direction of the wire 1 while the material to be processed 3 is being cut with the wire 1. Abrasive grains of a processing liquid 5 effectively get into the wedge-shaped space 10 and thoroughly work on the part to be cut so that the processing accuracy and processing efficiency of the material to be processed 3 can be enhanced. Furthermore, the pressing enables to eliminate the tilt in a plural number of thin plates at a part where the processing is completed, retain a regular spacing for the gap after cutting and securely prevent scratches or cracks developing on the processed surface of the material to be processed 3 with the wire 1 when the wire 1 is pulled out on completion of the processing.