Laser marking and engraving processes are very much important industrial micro-applications. The effects of process parameters such as laser power scan speed, frequency and fill spacing on the laser deep engraving of AISI 1045 stainless steel has been studied here. The optimum parameter conditions for minimization of the surface roughness and maximization of the engraving depth are also found out in this study. An experimental study consisting of 108 different parametric combinations is carried out to find out the process parameters which contribute surface roughness and engraved depth. It is seen that both surface roughness and engraving depth significantly decrease with an increase in the scan speed and a decrease in the laser power.