To improve the cutting quality of comparatively thick conductive ductive material, in particular the cutting quality and cutting efficiency in the edge regions of stainless steel by detecting the variation of the value of electric resistance between a cutting head and a material to be cut and executing parameter control in a cutting process from this variation.

An electric resistance measuring device 9 is provided between the laser beam cutting head 1 or conductive laser beam nozzle 2 and the material 5 to be worked and connected to the mechanical control (parameter control) part 15 in the cutting process through a computer aided evaluating device 14 together with a capacitive range finder 13. During cutting work, the electric resistance between the laser beam nozzle 2 and the material 5 to be worked is continuously measured and drop of the electric resistance when the maintenance of a required cutting depth of the laser beam 4 becomes difficult is detected with the evaluating device 14. At that time, the presence of the distance between the laser beam nozzle 2 and the material 5 to be worked is also detected with the range finder 13, the relative speed between the laser beam nozzle 2 and material 5 to be worked and the output of the laser beam 4 are lowered so as to recover the electric resistance in a regular cutting work.