Many mechanical parts used for various purposes, including medicine and information communication, have complicated and thin shapes owing to their functions and designs. To machine thin parts with high accuracy, it is necessary to reduce the cutting force induced on the workpiece or clamp the workpiece in an optimal manner. In this study, a support method capable of supporting the strength by using a magnetic elastomer is proposed. To test the effectiveness of the proposed support method, the use of the approach when applying a magnetic elastomer was compared with a method using a core, the low-melting point alloy, the low-melting point alloy and the elastomer. The effectiveness of the proposed method was clarified experimentally.