In this paper, a reduced elasto-dynamic model of the robotic based milling process is presented. In contrast to previous works, it takes into account the interaction between the milling tool and the workpiece that depends on the end-effector position, process parameters and cutting conditions (spindle rotation, feed rate, geometry of the tool, etc.). To reduce the dimension of the problem, the robot dynamics is described as an equivalent mass-spring-damper system with six dimensions. This approach, based on the Rayleigh-Ritz approximation, aims at decreasing computational cost and at avoiding inaccuracy due to ill-conditioning in the full size model. To achieve a realistic modeling of the milling process, the machining efforts due to the interaction between robot, tool and working material are introduced into the robot model and calculated at each time instant. Using this global model that integrates the robot dynamics and the milling process particularities, it is possible to obtain the movement of the robot end-effector and corresponding quality of the final product (profile, macro geometry, etc.). In addition, this model allows selecting the best process parameters and avoiding the vibratory behavior of this machining system which can dramatically affect the milling quality. The developed model is applied to the behavior analysis of KUKA KR270 robot used for milling applications. This allows finding acceptable range for robot motion profile parameters.