Abstract: The theory of fractional calculus has been widely applied to model the viscoelastic behaviour of soils subjected to static loading. However, limited work has been carried out on using fractional calculus to describe the cyclic elastoplastic behaviour of granular soils. Hence, a fractional rate for strain accumulation of coarse granular aggregates under cyclic loading is proposed, based on the analysis of the deformation of coarse granular aggregates subjected to cyclic loads by using the theory of fractional calculus. A fractional order bounding surface plasticity model for coarse granular aggregates under monotonic and cyclic loads is developed. It is noted that there are ten parameters of the proposed model, which can be experimentally determined by the traditional triaxial compression tests. To further validate the model, a series of laboratory test results of different granular aggregates from several independent literatures is simulated. It is found that the proposed model can well capture the monotonic and cyclic stress strain behaviour of coarse granular aggregates. It can also well predict the cumulative deformation under long-term cyclic loading.