Stainless steel has numerous applications in medical, engineering and industrial fields. It is recognized as difficult to machine (DTM) material. Conventional machining is challenging and also environmentally-unfriendly. Therefore, in the present work, SS304 has been attempted to machine using coated carbide tools under dry environment. This paper reports the investigation conducted on analysis of the effects of machining parameters such as cutting speed, feed rate, and depth of cut on productivity (material removal rate) and surface quality (average surface roughness); and optimization of machining parameters for the best values of these machinability indicators. Taguchi L9 orthogonal array based experimentation has been done. ANOVA has also been conducted to verify the statistical fitness and significant parameters. Grey relational technique has been used for optimization. Dry machining of SS304 at optimum combination of machining parameters i.e. cutting speed: 70m/min; feed: 0.1mm/rev; depth of cut: 1mm resulted in the optimized values of machinability indicators i.e. material removal rate- 116.67 mm³/s and average surface roughness- 1.99 µm.