A successful model for off-road tyres must be reliable, efficient and capable of reproducing and predicting the main system phenomena. Mathematical models are proposed for longitudinal, lateral and combined lateral and longitudinal force generation characteristics of off-road tyres. For a better understanding of off-road tyre behaviour, the study of the interaction between the tyre forces and those generated by the deformed soil is very important. Details of the force system in the contact patch, therefore, are used as a basis for developing models for the prediction of the tractive performance and comering characteristics of off-road tyres. Previous work of the relevant literature pertaining to tyre behaviour is reviewed to provide the reader with background information on off-road tyre characteristics. Various models for off-road tyres of differing degrees of complexity but which all incorporate the key features of off-road tyre problems are then developed. Previous methods of analysing the combined lateral and longitudinal forces generated by off-road tyres on deformable surfaces are investigated. A modified version of a previous model is then proposed which is based on a different and original method for investigating tyre behaviour in the contact region. An entirely new model is then developed which is based on a modification of the "multi-spoke" tyre model used for road vehicle studies. Predicted results are compared with those obtained from other models and with reported experimental data. The usefulness of such models is in problems involving the steering, braking and handling behaviour of off-road vehicles. Hence, the models are formulated so that they can be applied to such vehicle problems by enabling lateral and longitudinal forces on the tyre to be predicted from any combined conditions of wheelslip, wheelskid and slip angle. The proposed models provide an improved qualitative description of behaviour in the contact region. Although slightly more complex than previous models, the computational load is nevertheless sufficiently small that the tyre models can conveniently be incorporated in off-road vehicle handling models. Suggestions for future recommendations are discussed with particular reference to improving the predictive models and for a possible extension of the study to generate more detailed practical results for tyre forces under controlled experimental conditions.