A hybrid thermal cutting apparatus has both a laser head and a plasma torch, both of which can be controlled independently, can perform both laser processing and plasma processing, thus reducing the running costs. A large number of cutting lines for cutting out various types of manufactured products from plate materials are classified into a laser cutting type and a plasma cutting type, according to the cutting length, whether they are the external periphery of manufactured products or apertures, the size of the manufactured products or the apertures, the required process accuracy, the plate thickness, or the like. The lines of the laser cutting type are cut by laser processing, while the lines of the plasma cutting type are cut by plasma processing.