In this paper, a new open-loop model for a Magneto-Rheological (MR) based actuator is presented. The model consists of two parts relating the output torque of the actuator to its internal magnetic field, and the internal magnetic field to the applied current. Each part possesses its own hysteric behavior. The first part uses an open-loop Bouc-Wen model to relate the output torque to internal magnetic field. The second part uses a novel nonlinear adaptive observer that relates the internal magnetic field to the applied current. The model facilitates accurate control of the actuator using its input current. It also eliminates the need for force/torque sensors for providing feedback signals. The accuracy of the constructed model is validated through simulations. The overall model as well as each part of it is assessed against a widely accepted hysteresis modeling approach, known as the Preisach model and its advantages are highlighted. The second part of model is also compared to Bingham model which has been broadly employed in modeling of MR fluid dynamic. Bouc-Wen model shows higher accuracy in capturing hysteretic behavior of MR fluid in comparison to non-hysteretic Bingham model. Experimental results using the prototyped actuation mechanism further verify the accuracy of the model and demonstrate its effectiveness.