In order to investigate the influence of process parameters on the hole geometric features, experiments were conducted based on response surface methodology (RSM) as one of the most useful design of experiments (DOE) approaches. Frequency of the laser beam (80 to 240 Hz), duty cycle (20.00 to 40.00%) and laser power (100.00 to 200.00 W) were considered as independent variables, while the entrance and exit hole diameters and their circularity as well as the hole taper were raised as process outputs. The experiments were performed on samples of thin AMS 5510 stainless steel 321 sheet with thickness of 0.01 inch by a 500.00 W fibre laser. The results indicated that the entrance hole diameter and hole taper decrease when the laser pulse frequency increases and laser power decreases. Also, laser frequency has a double reaction before duty cycle and laser powers on circularity of entrance hole. Minimum hole taper, minimum entrance diameter, and maximum circularity of entrance hole were considered as optimization criteria. Verification experiments were carried out to analyse the results obtained via software.