To provide a working machine and a working method for a sheet material, by which, even when a workpiece holder interferes with a working head, the sheet material is fed without generation of displacement of the sheet material so that working is conducted within the grasping area of the workpiece holder.

A sheet material feeding means 3 is provided with a sheet material feeding member 5, which moves back and forth, right and left, and three or more workpiece holders 6, which advance and retreat back and forth. A control means 4 on sheet-material feeding judges sufficiency of such a condition that either of the workpiece holders is in a retreating state and a working head 2 interferes with the area of a sheet material W, which any of other workpiece holders grasps, when feeding the sheet material to a next positioning point. When the condition is satisfied, after making a sheet-material feeding member take an escape action backward, a right and left movement for feeding the sheet material to the next positioning point is conducted. Thereafter, the workpiece holder in the retreating state is moved back forward to grasp the sheet material. After the sheet material is grasped in this way, the workpiece holder that interferes with the working head is made to retreat backward, and the sheet material feeding member is made to move back by the distance of the backward escape action.