The development of crystallographic preferred orientation in a single-layer buckling assembly has been numerically simulated using an explicit, finite difference computer code, FLAC. The model treats the materials in the single competent layer and the embedding less competent matrix as a polycrystalline aggregate with one slip system, which exhibits elastic-perfectly-plastic behaviour, and assumes dislocation glide as the dominant strain accommodation mechanism. The results show that the preferred orientation of slip planes is much better developed in the less competent matrix than in the buckled competent layer. This correlates with the low strains developed in the layer and the high strains in the matrix. The competency contrast in the model also influences the fabric development, since changing the contrast effectively alters the final buckle size and strain distributions. The patterns of the preferred orientations vary throughout the assembly, showing different orientation relationships to the fold axial plane. The slip planes are generally preferably oriented approximately parallel to the local principal extension direction.