A three-dimensional dislocation cellular automaton model is developed to study the evolution of dislocation configurations in FCC single crystals. Crystallographic {111} slip planes with three-fold symmetry are discretized into equilateral triangular patches with sides along 110 directions. These patches slip provided there is a sufficient driving force associated with reduction in system energy. Perfect 110/{111} dislocations are considered. The resulting variables are the triangular patch size and dislocation core cut-off, measured relative to Burgers vector magnitude b. Three examples involving operation of a Frank–Read source are chosen to highlight the benefits and drawbacks of the method. A benefit to discretization is that dislocation evolution may be analysed via spatial averaging over collections of patches, so that the discrete versus continuum nature of the results may be studied. Further, dislocation reactions and cross slip are accommodated easily and, in principle, Monte-Carlo schemes can be integrated into the evolution formalism. A drawback is that collections of patches do not reflect a smooth variation in configuration so that artificial fluctuations in dislocation line length and direction can result. Overall the discrete nature of the method is attractive for incorporating the kinetics of thermally activated states and for simplifying the range of geometries and threshold criteria associated with dislocation reactions.