The behaviour of granular materials is complex. Unlike all other engineering materials their volume change does not only depend upon an applied mean stress, but also on the change in shape of the body. This complexity in the behaviour makes it difficult to develop useful constitutive equations which describe the behaviour. Many constitutive models exist for granular materials. Using an established approach new models, suitable for simulating small cyclic strains, are presented within this thesis. The basis for these models is a new dilatancy rule. By setting the volume strain proportional to the square of the shear strain it is possible to develop a yield surface which is characterised by kinematic hardening. All models are developed from an energy balance. In the past this has only been made up of two terms, the work done and the energy dissipated as a result of plastic deformation. Including a term which expresses the rate at which energy is stored during elastic deformation allows the simulation of cyclic shear loading on granular materials. These simulations show pleasing agreement with experimental results. To account for the nonlinear plastic behaviour seen in granular materials, hardening rules for a two dimensional case are developed. These introduce critical states and maximum densities into the formulation. By modelling the results of cyclic shear tests on assemblies of rods, it is shown that the hardening rules are not only useful for modelling soils, but also other materials, such as pastes. Finally a dissipation function which has been suggested by Houlsby is used to formulate a new model. Again this is based on the successful dilatancy rule used in the previous models. By combining the dissipation function of Houlsby and the quadratic dilatancy rule, a yield surface and flow rules are developed which successfully model the circular loading of sands.