This thesis develops and experimentally verifies a model of a two arm robot with highly elastic arms. The model is later used in this research to evaluate control algorithms. The model includes the effects of gravity. The dimensions of the arms are chosen to maximize the coupling between the flexible and large scale motion of the robot. The model is then linearized and a new analytical solution is presented for the natural frequencies and mode shapes of the robot at given equilibrium positions. This analytical solution is then compared to the assumed mode shape solutions to determine the accuracy relative to the number of assumed modes included in the model. An experimental test rig is built and tests are conducted to verify the model. A number of different amounts of end mass and torsional stiffness at the joints are used during the validation. For 12 cases tested, the measured first four natural frequencies are within ±7% of the frequencies predicted by the model with an average error of only 2.89%. Finally, the model is used to design a control algorithm for end effector control of the robot using a torque input at each of the two joints. An optimal control algorithm developed using LQR with the prescribed degree of stability method results in effective end effector control with short response time and little overshoot.