Fluid mechanics plays a crucial role in the design of hydraulic dampers and actuators. These devices are necessary to ensure smooth operation of high speed machines and vehicles. Currently, passive dampers are commonly used due to their cost-effectiveness, but they are less adaptive. On the other hand, active dampers are highly effective as they respond quickly to changes in environmental stimuli but come with a higher price tag. As a result, researchers are investigating semi-active dampers as a viable solution to achieve a balance between affordability and effectiveness in the design of vibration attenuating systems. Magneto rheological (MR) fluid actuators and dampers (semi-active dampers) are used in a number of vehicle dynamic applications. Popular models of MR devices are Bingham and Bouc-Wen which can be integrated in system level vehicle dynamics models. Several approaches have been used to solve these system level models using semi-analytical and numerical methods. This article explores traditional model based approaches to characterize magneto rheological devices. Comparison of different numerical methods for dynamic response is investigated in this article.