The distinct element method (DEM) is an approach to modelling and simulation well suited to the study of discontinuous phenomena. By tracking each element individually and dealing explicitly with every interaction among the elements, the DEM allows one to deduce statistical behaviour of the assembly. Realistic simulation of granular materials has largely benefited from this relatively recent approach. In particular, it is now possible to address specific phenomena such as arching effects, flows and packings in three dimensions and to make them observable, which is impossible or at least extremely complicated to achieve with physical experiments. Two major issues arise in the context of DEM: efficient detection of the interactions between the grains and numerical modelling of the physical contacts. This paper focuses on the former by presenting an efficient collision detection scheme for spherical grains of various sizes based on a dynamic three- dimensional Delaunay triangulation. Aside from the theoretical and practical discussion of this scheme, the remaining requirements for a complete DEM simulation are also addressed. Finally, examples are given to illustrate the potential of this approach.