The aim of this work is to relate the cutting edge quality parameters (responses) namely: upper kerf, lower kerf, ratio of the upper kerf to lower kerf and cut edge roughness to the process parameters considered in this research and to find out the optimal cutting conditions. The process factors implemented in this research are: laser power, cutting speed and focal point position. Design of experiment (DoE) was used by implementing Box-Behnken design to achieve better cut qualities within existing resources. Mathematical models were developed to establish the relationship between the process parameters and the edge quality parameters. Also, the effects of process parameters on each response were determine. Then, a numerical optimization was performed to find out the optimal process setting at which the quality features are at their desired values. The effect of each factor on the responses was established and the optimal cutting conditions were found.