This paper presents a new, detailed dynamics model of a novel type of actuators based on tendons with integrated springs that allows for offline adjustment of the stiffness characteristics. Like other cable or belt actuators, the elastic tendon actuator allows to radically reduce the link inertia by placing the motors near the robot base. But by additionally integrating springs in the tendons, the motor and the joint are elastically decoupled, which increases the lifespan of the tendons and the safety of the actuator. A detailed mathematical model of the actuator is derived taking tendon slackening effects into consideration. The result is a degressive stiffness curve that depends on the pretension force of the integrated tendon springs. The derived model is validated against static and dynamic experimental measurement data of a robot arm equipped with elastic tendon actuators.