This paper introduces a stochastic structural modelling method that honours interpretations of both faults and stratigraphic horizons on maps and cross-sections in conjunction with prior information, such as fault orientation and statistical size-displacement relationships. The generated stochastic models sample not only geometric uncertainty but also topological uncertainty about the fault network. Faults are simulated sequentially; at each step, fault traces are randomly chosen to constrain a fault surface in order to obtain consistent fault geometry and displacement profile. For each simulated fault network, stratigraphic modelling is performed to honour interpreted horizons using an implicit approach. Geometrical uncertainty on stratigraphic horizons can then be simulated by adding a correlated random noise to the stratigraphic scalar field. This strategy automatically maintains the continuity between faults and horizons. The method is applied to a Middle East field where stochastic structural models are generated from interpreted two-dimensional (2D) seismic lines, first by representing only stratigraphic uncertainty and then by adding uncertainty about the fault network. These two scenarios are compared in terms of gross rock volume (GRV) uncertainty and show a significant increase in GRV uncertainty when fault uncertainties are considered. This underlines the key role of faults in resource estimation uncertainties and advocates a more systematic fault uncertainty consideration in subsurface studies, especially in settings in which the data are sparse.