Through a chain of rigid actuators, roboticists are capable to closely replicate the morphology and the kinematics of anguilliform swimmers like lampreys. However, a robot is mainly composed of rigid structures while the animal’s body is composed of soft tissues with viscoelastic mechanical properties. In this work we use a simple muscle model to generate an input torque signal that drives the robot’s motors providing them with viscoelastic properties. The model has three components. An activation gain that represents the active element, stiffness and damping terms that represent the passive elements. Twenty representative tests were run and a second order model was fitted following the Response Surface Method. Using this methodology the steady state velocity, acceleration, power consumption and Cost of Transport (CoT) are evaluated as proxies for the swimmer’s performance. Our results show that different velocities can be achieved only by modulating the activation signal (i.e. without taking into account the stiffness and damping values). However, high velocities come at the cost of high power consumption and CoT. Modulating stiffness then helps lower CoTs and power consumption during steady state swimming, reaching a performance similar to those of a real animal. Interestingly, the stiffness also improves the peak acceleration which is important for escape responses. On the other hand, increments of damping have improvements in CoT. However, the internal damping of the mechanical components of the robot, presents higher damping values than their animal counterparts. Our results show that a swimming robot using a muscle model is able to reproduce the dynamics of an eel swimming at low frequency and velocity.