Three-dimensional numerical models of neutral (i.e. slip-parallel) relay zones on normal faults that cut massive sandstone host rocks have been constructed using the distinct element method code, Particle Flow Code in 3-D (PFC3D). The models successfully reproduce the geometries, displacement profiles and strains observed in natural relay zones. In contrast to boundary element method simulations, the modelled relay ramps dip towards the hanging wall, consistent with observations of most natural relay zones. The modelling shows that relay zones are stable structures that ‘grow’ by progressive rotation of an approximately planar relay ramp without significant propagation of the relay-bounding faults prior to breaching. Stable growth is terminated when a breaching fault propagates across the top or bottom of the relay ramp. Breaching fault propagation is not instantaneous and the ramp continues to rotate, and therefore transfer displacement between the relay-bounding faults, until they become fully hard linked. Following hard linkage, displacement is accommodated by slip on the through-going fault surface. The modelling results confirm previous conceptual models of relay growth and breaching based on geometric and kinematic analysis of natural relay zones.