The apparent slow development and uptake of smart fluid technology has been suggested to be partly due to the inherent non-Newtonian nature of the fluids. To improve matters, it is desirable to determine practical pre-prototype performance. This is possible with a continuum approach and by solving the basic governing equations. Analytical methods are limited to the simplest devices. Therefore, the most practical way forward was hypothesised to be with existing highly developed CFD packages. This thesis investigates the possibility of using CFD to model smart fluid flow. \nInitially, the feasibility of modelling basic isothermal, steady, one-dimensional flow was investigated. The procedure was then extended into modelling two-dimensional flow. Here the CFD method was used to investigate some practical problems involving a second perpendicular flow to naturally replace heated fluid. In addition, a smart fluid seal problem was resolved. \nThe procedure was extended in order to investigate unsteady flow. For a CFD clutch run-up model, problems were identified in an existing analytical solution. To help verify the CFD model, an experimental study was carried out. For the results to agree, an inertial boundary condition has to be developed that allows the inertia of the outer rotor to be included in the CFD model. Here the fluid dynamics affect the rotor dynamics and vice versa. \nA constitutive model of a viscoelastic form was found to be most appropriate for modelling sudden changes in excitation. This allowed CFD responses to correspond well with experimental results carried out on an ER fluid Rayleigh step-bearing rig. \nThe usefulness of CFD for determining the generation and transfer of heat, in addition to temperature distribution, was investigated by comparing CFD results to both experimental and semi-empirical analysis. \nIn conclusion, CFD as a pre-prototyping tool promises to be very useful. However, it is only as good as the continuum assumption allows it to be. The procedure is also limited by how well the constitutive equation can be determined and by the detail and quality of fluid property data.