Geostatistical modeling of reservoir facies and petrophysical properties (e.g. porosity and permeability) must be performed in a pre-faulted, deposition space in order to reproduce the true spatial correlations of these properties. A transformation function is therefore required to bring the data from the current position of the reservoir into the modeling space where experimental variograms are computed; reservoir properties are then stochastically simulated in the deposition space and mapped back to the real space. Current reservoir modeling practice uses a stratigraphic grid to conform to the reservoirs structure (bounding horizons and faults). The (i, j, k)-indexing of the nodes of the cells is used as a discretization of a curvilinear coordinate system which acts as the transfer function to the deposition space. This leads to a very strong underlying assumption: the geological distances (in the deposition space) are a function of the (i, j, k)-indexing. In the presence of non-vertical faults, the cells of the stratigraphic grids are either stretched or squeezed, violating this assumption. Moreover, in the presence of complex structural geology, these grids simply cannot be constructed without tremendous simplifications. The new proposed approach uses a 3D parameterization of the subsurface yielding a grid that minimizes the distortions of distances imposed by geostatistical simulation algorithms. These new Geologic Grids allow the construction of robust reservoir models whatever the structural complexity of the reservoir. Additionally, they guarantee the accurate mapping and upscaling of reservoir properties into either structured or unstructured Flow Simulation Grids. They also enable the creation of structured Flow Simulation Grids in which faults are defined as stair-steps allowing representation of the complete reservoir structure and ensuring orthogonality of cells.