Laser drilling has swiftly become an economical and well-regulated substitute to conventional hole drilling methods such as wire EDM, punching, broaching, or other prevalent destructive processes, because of cleanliness, accurate results, precise holes, fast material removal rate, and possibility to make holes. Prompt expansion of laser technology in current years gave us facility to regulate laser input factors such as lamp current, pulse frequency, air pressure, and pulse width. The dimensional accuracy and quality of holes are very important for some specific applications of holes. Circularity of drilled hole at entry and exit, and taper are very important attributes which influence the quality of a drilled hole in laser drilling. For this reason, the experimentation based on central composite design is carried out on austenitic stainless steel for examining the effect of laser parameters, i.e., lamp current, pulse frequency, gas pressure, and pulse width, on the quality of drilled holes. A total of 31 experiments were carried out. Later, the models were predicted for output responses using response surface methodology and then tested for adequacy. It is found that the response surface methodology (RSM) predicted models are in close agreement with the experimental values. Hence, the models may be further used for optimization of process parameters using evolutionary algorithms.