A planar-member machining system comprising a laser machine and a workpiece support the laser machine having: a workpiece rack, a laser head that is adapted to machine in a first machining region the workpiece placed on the workpiece rack while the laser head moves, with respect to the workpiece in a stationary state, in a one direction along a horizontal plane and in another direction along the horizontal plane and perpendicular to said one direction; and an elevator, characterized in that the system further comprises a second machine and a carrying apparatus, the workpiece rack is configured to travel with a planar workpiece placed thereon, the elevator is configured to locate the workpiece in the first machining region by raising and lowering the workpiece rack with the workpiece placed thereon; the second machine includes a machining tool for machining the workpiece in a second machining region different from the first machining region, and being set midway in a course through which the workpiece is carried by the carrying apparatus; the workpiece support is configured to support the workpiece in the first machining region either by receiving and having placed thereon the workpiece that has been placed on the workpiece rack in the first machining region or by passing to and placing on the workpiece rack the workpiece that has been placed on and supported by the workpiece support; and the carrying apparatus is adapted to carry the workpiece by holding the workpiece placed on the workpiece support and transferring the workpiece on the workpiece support between the first machining region and a region opposite to the first machining region with respect to the second machining region while the workpiece support is supporting the workpiece, wherein the machining tool of the second machine is configured to move in a crossing direction that crosses a direction in which the workpiece is carried by the carrying apparatus. a workpiece rack, a laser head that is adapted to machine in a first machining region the workpiece placed on the workpiece rack while the laser head moves, with respect to the workpiece in a stationary state, in a one direction along a horizontal plane and in another direction along the horizontal plane and perpendicular to said one direction; and an elevator, characterized in that the system further comprises a second machine and a carrying apparatus, the workpiece rack is configured to travel with a planar workpiece placed thereon, the elevator is configured to locate the workpiece in the first machining region by raising and lowering the workpiece rack with the workpiece placed thereon; characterized in that the system further comprises a second machine and a carrying apparatus, the workpiece rack is configured to travel with a planar workpiece placed thereon, the elevator is configured to locate the workpiece in the first machining region by raising and lowering the workpiece rack with the workpiece placed thereon; the second machine includes a machining tool for machining the workpiece in a second machining region different from the first machining region, and being set midway in a course through which the workpiece is carried by the carrying apparatus; the workpiece support is configured to support the workpiece in the first machining region either by receiving and having placed thereon the workpiece that has been placed on the workpiece rack in the first machining region or by passing to and placing on the workpiece rack the workpiece that has been placed on and supported by the workpiece support; and the carrying apparatus is adapted to carry the workpiece by holding the workpiece placed on the workpiece support and transferring the workpiece on the workpiece support between the first machining region and a region opposite to the first machining region with respect to the second machining region while the workpiece support is supporting the workpiece, wherein the machining tool of the second machine is configured to move in a crossing direction that crosses a direction in which the workpiece is carried by the carrying apparatus.