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A general overview is presented on applications of the discrete element method (DEM) to granular media. A literature survey is performed of static and dynamic simulations using random arrays of compliant particles, and forty‐two references published mostly in the last ten years are identified and categorized according to a number of relevant criteria. It is concluded that the interest in the use of the technique is rapidly increasing in the research and engineering community, with applications concentrated in soil mechanics, rock mechanics, grain flow and engineering problems. Additional studies and verifications of some numerical aspects of the DEM technique are suggested including parametric studies and comparisons. Program CONBAL‐2 (CONTACT + TRUBAL in 2D) developed by the authors based on TRUBAL created by Strack and Cundall, is described. CONBAL‐2 uses the complete Mindlin solution for the contact between two spheres and thus can be used for small strain and cyclic loading. The program is applied to study the cyclic response of uniform, medium dense to dense rounded quartz sand. Cyclic strain‐controlled loading at constant volume is applied to isotropically consolidated, random arrays of 531 spheres, using cyclic strains ranging from 10–4% to 10–1%. The calculated shear modulus, Gmax, constrained modulus, D, and Poisson's ratio at small strains are correlated with the confining pressure, the porosity of the array, and the coordination number. The calculated variations of secant modulus and damping ratio with cyclic strain compare favourably with the experimental results on sands compiled by Seed and Idriss. Finally, ‘pore water pressure buildup’ and cyclic stiffness degradation of the material with number of cycles is calculated at a cyclic strain of 10–1%, and the prediction is found to represent closely cyclic undrained experiments on sands. The existence of a threshold strain, yt ≈ 10–2%, found experimentally, is also predicted by the simulations.