Product quality, productivity and organizational goodwill are often the major concern of every production or manufacturing unit. These criteria, more especially product quality, cannot readily and effectively be met through dependence on the skills of an operator. Hence, the need for optimization in order to identify the best process condition, derived from parametric combinations of process variables, for the manufacturing process. The work presented concerns an aspect of a series of hard turning experiments on 41Cr4 alloy structural steel conducted to model, predict and optimize the machining induced vibration, and the surface roughness as functions of the cutting speed, feed rate, and the tool nose radius. The response surface methodology, based on the central composite design of experiment is employed in the study, and analysis of the generated data performed with the aid of Design expert 9 software. A quadratic regression model was suggested as best fits for both the machining induced vibration and surface roughness data. These were confirmed by analyses of variance, which also revealed the tool nose radius and cutting speed, as well as the feed rate and cutting speed to be important factors that determine changes in the machining induced vibration and surface roughness, respectively. The optimum setting of the tool nose radius at 1.72301 mm, feed rate at 0.15 mm/rev, and the cutting speed at 311.075 rev/min minimized the machining induced vibration to a value of 0.08 mm/min 2 and the surface roughness to a value of 4.74 µmm.