Differential settlement along ballasted railway tracks is one of the main factors that force maintenance work. The elasticity of the sleeper (the railroad tie) plays a key role in transferring the wheel-rail contact forces to the ground, and thus, impacts the long-term track settlement due to the occurring local pressure distribution. A deeper physical understanding of the interaction between the railway sleeper and the ballast can help to improve the railway infrastructure and thereby reduce maintenance activities significantly. Due to the discrete nature of railway ballast, the discrete element method (DEM) is considered a suitable and widely used numerical tool to gain insight into the physical phenomena at particle level and to simulate the bulk behaviour of ballast. In recent DEM related railway track research, the sleeper is either modelled as a rigid body, built up by bonded particles or implemented by a complex coupling method. Since sleeper elasticity significantly impacts the dynamic interaction of the sleeper with the ballast bed, efficient DEM simulations with accurate elastic sleeper models are needed. In this thesis a method is presented that uses the particle facet model (PFM) to design an elastically deformable sleeper. The PFM uses nodes, cylinders, and so-called PFacets to construct flexible objects and was initially utilised to model elastic roots, grids, and membranes with a smooth surface. This approach is adapted to replicate a smoothed surface elastic sleeper without the need for coupling techniques. This way, railway track simulations can be carried out that consider the effects of sleeper elasticity on the discrete railway ballast realistically. DEM simulations in a box-test setup were carried out in which the elastic PFM sleeper was placed on a compacted ballast bed and then cyclically loaded. The computed pressure distribution at the sleeper-ballast interface, the sleeper deflection profile and the settlement were in qualitative agreement with the literature. In contrast to rigid sleeper models and numerical tools that consider the ballast as a continuum, the simulations have shown that the aforementioned results heavily depend on the initial configuration of the ballast bed. The proposed modelling method offers an realistic integration of elastic sleepers into ballasted railway track DEM simulations and thereby improves the understanding of the physical effects resulting from the sleeper's elasticity. Numerical studies of complex railway track regions where the sleeper´s mechanical properties are decisive, as found in curves or turnouts, are thus made possible.