Whereas more and more reservoir studies use geostatistical simulations to represent petrophysical uncertainty, geological structures are often kept frozen in 3D reservoir modeling. Existing methods which eventually perturb geological structures act directly on the reservoir grid, hence are limited by current flow simulators. Instead, we use a flexible parametric model to stochastically perturb fault and horizon surfaces. We propose two methods to transfer this perturbation onto a volumetric model while maintaining its geometric consistency: - A new extension of simple constrained deformation is applied to a stratigraphic grid, which can then be used in mainstream flow simulators. - A method to perturb both the horizons and fault geometries in a geo-chronological model is also described. This clears the way to realistic structural uncertainty handling in new generation flow simulators.