Discrete element modelling of a monotonic triaxial test is carried out with the aim of studying the stress-strain response of railway ballast in a large-scale tester. The latex membrane of the tester is modelled via a lattice of bonded particles to investigate the effects of membrane stiffness on the stress-strain response. The confining pressure application through the membrane is achieved via individual forces applied to the membrane particles, giving rise to a uniform, radially inward, equivalent stress. This modelling approach leads to a close agreement with published experimental data. A coarse-graining analysis of the numerical results is performed to study the evolution of the stress state in the numerical sample.