This paper presents the design of a lightweight robot arm intended for safe physical human-robot interaction. The robot arm design combines tendon actuation with elasticity in the tendons to achieve a significant reduction in mass and passive compliant behavior. The use of elastic tendons in all joints in order to gain maximum safety and performance properties, however, results in a significant increase of the model complexity with oscillatory behavior and kinematic coupling of the joint equilibrium positions. Therefore, special effort needs to be made to model the robot arm dynamics, which is an essential basis for model-based algorithms utilizing and fully exploiting the particular properties of the robot arm. This paper therefore derives the full dynamics model of the robot arm with focus on the nonlinear elastic tendon actuators, the kinematic tendon coupling, and modeling complexity reduction by reflecting all model parameters to the joint space. The resulting model is validated by comparing the identified simulation model with experimental data of an application-related pick-and-place trajectory and a trajectory with undamped oscillating motions of the robot arm.