Laser cutting is a popular manufacturing process utilized to cut various types of materials economically. The width of laser cut or kerf, quality of the cut edges and the operating cost are affected by laser power, cutting speed, assist gas pressure, nozzle diameter and focus point position as well as the work-piece material. In this paper CO2 laser cutting of stainless steel of medical grade AISI316L has been investigated. Design of experiment (DOE) was implemented by applying Box-Behnken design to develop the experiment lay-out. The aim of this work is to relate the cutting edge quality parameters namely: upper kerf, lower kerf, the ratio between them, cut section roughness and operating cost to the process parameters mentioned above. Then, an overall optimization routine was applied to find out the optimal cutting setting that would enhance the quality or minimize the operating cost. Mathematical models were developed to determine the relationship between the process parameters and the edge quality features. Also, process parameters effects on the quality features have been defined. Finally, the optimal laser cutting conditions have been found at which the highest quality or minimum cost can be achieved.