In Solid Modeling, a boundary representation (b-rep) defines solids by their bounding surfaces, providing an efficient volume description. Building on this representation, we present the notion of a Sealed Geological Model. In such a model, the geological surfaces define a partition of the domain of interest into regions; analytic functions can be defined in these regions to describe the spatial variations of the subsurface properties. Such descriptions can be used in Geophysics, 3D GIS, and for discretization purposes. In addition to the b-rep representational validity conditions, Sealed Geological Models must satisfy conditions of geological consistency. Bearing these conditions in mind, we describe a methodology to create and modify the shape of such sealed models interactively. We use the hierarchical relationship between geological surfaces to help reshape the contact between a fixed surface (a surface that other surfaces can slide along, such as a fault, erosion surface, or salt top) and a secondary deformable surface (e.g. horizon, older fault). Although designed to meet the demanding requirements of interactive model editing, our methodology could also make use of displacement vectors computed by an automatic process such as tomographic inversion or 3D balanced unfolding.