H13 tool steel is frequently used in hot work dies, hot forging, hot extrusion, and mold materials for casting ferrous and nonferrous materials. Surface roughness is of key importance in case of dies and moulds, as it insures the finish of the final product. After studying the work done by the researchers in field of machining and its impact over surface roughness, it was found that machining behaviour of H13 steel at the annealed state is not being studied. The surface finish obtained during turning of H13 steel are not studied on a greater scale, so the present study includes the analysis of finish (surface roughness) generated. Turning operation is carried out on the CNC machine at dry condition with an aim to find systematically the effect on surface roughness by distinct machining variables like feed rate, depth of cut and speed. RSM model using Box Behnken design is used to predict the roughness developed during turning of annealed H13 steel using carbide tool. It was found that feed rate and the depth of cut have a direct relation with the surface finish and the value of surface roughness increases with increase in these parameters. On the other side, cutting speed has a less impact over the surface roughness & is inversely related.