Abstract : The precision - speed coupling is a major problematic for 5 axis milling. The precision respect generally compels the machine to slowdown. Moreover, the tool axis orientation algorithm does not consider the machine tool behaviour. These thesis works aim at two objectives: - Optimise the machine tool behaviour by modifying the tool axis orientation in the machine coordinate system. - Guarantee the geometrical constraints respect of the tool axis orientation. An optimisation under constraints is proposed. The objective function uses a simplified model of the machine tool behaviour. The Domain of Admissible Orientation concept is then defined to constrain the tool axis orientation in the part coordinate system then in the machine coordinate system for the optimisation to be achieved. The optimisation method is compared to alternative methods using criteria of computation speed and efficiency.