Abstract: In a thermal cutting machine such as plasma cutting machine or a laser cutting machine, control of the moving speed of a cutting head (24) is improved so as to increase throughput of the cutting machine with increase in cost restricted. Products are cut out one by one from a plate member (14) while a cutting head (24) is moved relative to the plate member (14) on a table (12). In this process, when the cutting head (24) is fast-forwarded without performing cutting to a position at which cutting of each product starts, the speed of movement in the direction (Y-axis direction) along a short side of the table (12) is controlled at a speed higher than that of the movement in the direction (X-axis direction) along a long side of the table. The pattern of a sequence of cutting out the products from the plate member (14) is a meandering pattern in which reciprocation in the Y-axis direction dominates and the movement in the X-direction is one time one way.