Laser cutting process is well suitable process for the cutting applications of high strength temperature resistant alloys, that are very difficult to cut with conventional process. Moreover, the lasers are widely using now-a-days for variety of cutting operations in many varieties of industries. Because of its complex nature of its operation, it is not easy to control so as to get the desired quality of cut in case of laser beam cutting process. This necessitates the importance of research to be carried out on the various processes i.e cutting, drilling, and welding etc by using the laser apparatus. The research mainly concentrated on the conduction of experiments i.e the cutting operation on Haste alloy C276 with CO2 laser beam. Total 31 trails are done using the CO2 laser beam apparatus. Laser power, speed, gas pressure and focal distance were the parameters chosen to vary. The outputs measured are surface roughness and the burr height which are direct measure to the quality of the cut surfaces. Two dimensional plots are plotted and analyzed the reasons for the increase or decrease of output with either the increase or decrease of input process parameters. Also, 3D plots are plotted to know the interactions.