This paper considers control of an elastic robotic arm of two links based on non–linear inversion and pole assignment for stabilization. The design is performed in two steps. First, based on non-linear inversion, a non–linear controller is designed for the trajectory control of the joint angles using joint torquers. The inverse controller accomplishes trajectory control of the joint angles, this excites the elastic modes of the arm. In order to damp the elastic oscillations, a stabilizer is designed for a linearized system about the terminal state using the pole assignment technique. In the closed–loop system, first the inverse controller acts when a command is given, and the stabilizer automatically switches when the joint angle trajectory enters a specified neighbourhood of the final commanded position. Simulation results are presented to show that in the closed–loop system accurate joint angle trajectory tracking and elastic mode stabilization can be accomplished in spite of payload uncertainty in the system.