An approach is presented to optimize the surface roughness in high-speed finish milling of 7050-T7451 aeronautical aluminum alloy. In view of this, the multi-linear regression model for surface roughness has been developed in terms of slenderness ratio, cutting speed, radial depth-of-cut and feed per tooth by means of orthogonal experimental design. Variance analyses were applied to check the adequacy of the predictive model and the significances of the independent input parameters. Response contours of surface roughness were generated by using response surface methodology (RSM). From these contours, it was possible to select an optimum combination of cutting parameters that improves machining efficiency without increasing the surface roughness.