The material point method, which combines features of finite-element and particle discretisation methods, has been extended to solve coupled flow-deformation problems in granular media. The method is applied to simulate the construction and failure of the Aznalcóllar dam. The brittle foundation clay is characterised by means of a strain-softening Mohr–Coulomb elasto-plastic model. The rupture process of the foundation is associated with a progressive failure mechanism. The model predicts the development of a localised shearing band that initiates at the toe of the dam at some intermediate stage of construction, and propagates downstream and upstream. The shape and position of the failure surface reproduce actual field observations.