A hard-sphere discrete particle model of a gas-fluidised bed was used in order to simulate segregation phenomena in systems consisting of particles of different sizes. In the model, the gas-phase hydrodynamics is described by the spatially averaged Navier-Stokes equations for two-phase flow. For each solid particle, the Newtonian equations of motion are solved taking into account the inter-particle and particle-wall collisions. The (2D) model was applied to a binary system consisting of particles of equal density, but different sizes where the homogeneous gas inflow velocity was equal to the minimum fluidisation velocity of the bigger particles. Segregation was observed over a time scale of several seconds although it did not become complete due to the continuous back mixing of the bigger particles by the bubbles. An analysis of the dynamics of the segregation in terms of mass fraction distributions is presented. When the particle-particle and particle-wall interactions were assumed to be perfectly elastic and perfectly smooth, segregation occurred very fast and was almost complete due to the absence of bubbles.