The purpose of this research project is to model the rheological behaviour of elastomers and elastomer compounds. Two elastomers (natural rubber, SMR 20 and chlorosulphonated polyethylene, Hypalon 40) and three different grades of carbon black at three different levels of loading were chosen for this study. Mixing was carried out with a Farrel Bridge BR Banbury mixer, followed by subsequent milling on a two-roll mill. Rheological measurements were made with parallel plate, cone and plate and Negretti biconical rotor TMS rheometers . . The effect of temperature on viscosity was investigated by determining the activation energy of viscous flow in terms of concentration and surface area of carbon black. Computer programs were developed to evaluate various parameters in the models by non-linear optimisation technique. The steady state flow behaviour of gum elastomers was fitted by the Bird-Carreau model and a thixotropic model. The thixotropic model was modified to non- Newtonian flow but proved to be intractable for fitting the rheological properties of mixed rubber compounds. Two new models for the viscosity and stress relaxation of filled compounds were then developed, which give very promising results.