Laser process parameters influence greatly the width of kerfs and quality of the cut edges. This article reports experiments on the laser plywood-cutting performance of a CW 1.5 kW CO2¬ Rofin laser, based on design of experiments (DOE). The laser was used to cut three thicknesses 3, 6 and 9 mm of plywood panels. The process factors investigated are: laser power, cutting speed, air pressure and focal point position. The aim of this work is to relate the cutting edge quality parameters namely: upper kerf (UK), lower kerf (LK), the ratio between upper to lower kerfs and the operating cost to the process parameters mentioned above. Mathematical models were developed to establish the relationship between the process parameters and the edge quality parameters, and special graphs were drawn for this purpose. Finally, a numerical optimization was performed to find out the optimal process setting at which both kerfs would lead to a ratio of about 1, and at which low cutting cost take place.