We consider the force control problem of a one degree-of-freedom flexible robot manipulator. We approximate the distributed parameter flexible structure by a finite number of rigid elements connected by means of torsional springs. We assume that the arm tip interacts with the environment under rigid, frictionless, point contact conditions. The kinematic (holonomic) constraints which hold when contact is established, are derived using the geometry of the problem. The free and constrained motion of the arm are predicted numerically using the Newmark integration method. Numerical result are compared to the empirical system response. The conventional energy principle method for predicting the maximum reaction force is demonstrated, along with a much more efficient method based on the evaluation of instantaneous velocity increments just after impact. The later assumes that velocities vary linearly between the time instants of initial contact and maximum force occurrence. Finally, a hybrid impact- force real-time controller for diminishing the impact effect is implemented and various design considerations are presented.