A set of stochastic mathematical models have been developed to simulate the residence time distribution of solids in the riser of a circulating fluidised bed. The models simulate the motion of single particles moving up and down the riser using a Markov chain. Two models are presented in detail: (i) a core-annulus solids interchange model, and (ii) a four zone model that follows from the fast fluidised bed hydrodynamic profile. Both discrete and continuous time versions are presented. Each model incorporates different sections to account for the different flow regimes that exist within a riser. Simulations are linked to actual experimental conditions using local particle transfer rates between each model section. Simulations are able to predict the influence of changes in the solids flux, riser height and riser exit geometry. The influence of core-annulus solids transfer is also investigated. Comparison with a range of experimental data is presented.