The question of whether layered sequences of sedimentary rock subjected to layer-parallel compression will fold or fault is investigated by means of mechanical modelling using the Finite Element Method. The model consists of a rigid basement, a weak visco-elasto-plastic décollement horizon and a relatively competent elastic–plastic cover sequence. Syntectonic erosion and sedimentation on the surface are included using a diffusion model. Numerical results show that folding is the dominant mode of deformation when the décollement horizon is relatively thick and has a low viscosity, when the upper layer has a relatively high elastic shear modulus and when the total thickness of the sequence is relatively small. If any one of these conditions is not satisfied, faulting dominates. Other parameters such as the angle of internal friction and cohesion influence the style of deformation but have little influence on the boundary between folding and faulting. Results are interpreted in terms of competing deformation instabilities. If fold amplification rates are large, folding dominates over faulting. If on the other hand, fold amplification rates are small, faulting dominates because stresses intersect the failure surface before significant fold amplification can occur.