Discrete element method (DEM) models to simulate laboratory element tests play an important role in advancing our understanding of the mechanics of granular material response, including bonded or cemented, particulate materials.Comparisons of the macro-scale response observed in a real physical test and a "virtual" DEM-simulated test can calibrate or validate DEM models.The detailed, particle scale information provided in the DEM simulation can then be used to develop our understanding of the material behaviour.It is important to accurately model the physical test boundary conditions in these DEM simulations.This paper specifically considers triaxial tests as these tests are commonly used in soil mechanics.In a triaxial test,the test specimen of granular material is enclosed within a flexible latex membrane that allows the material to deform freely during testing, while maintaining a specified stress condition. Triaxial tests can only be realistically simulated in 3D DEM codes, however analogue,2D, biaxial DEM simulations are also often considered as it is easier to visualize particle interactions in two dimensions. This paper describes algorithms to simulate the lateral boundary conditions imposed by the latex membrane used in physical triaxial tests in both 2D and 3D DEM simulations.The importance of carefully considering the lateral boundary conditions in DEM simulations is illustrated by considering a 2D biaxial test on a specimen of frictional unbonded disks and a 3D triaxial test on a bonded (cemented) specimen of spheres. The comparisons indicate that the lateral boundary conditions have a more significant influence on the local,particle-scale response in comparison with the overall macro-scale observations.