A black oil reservoir simulator was developed for hexahedral minti-block grids . An objectoriented approach for the design and implementation of the simulator was adopted . We discuss the general features and object-oriented (0/0) design of the simulator.Complexity in geological or well features in a reservoir model (e .g., faults, inclined and multi-lateral wens) entails non-orthogonal and/or unstructured grids in place of conventional Cartesian grids . To obtain flexibility in gridding as well as numerical efficiency, hexahedral minti-block grids are employed . These multiblock are locally structured and globall y unstructured.In general, one can always generate multiblock grids with matched grids at block boundaries, and that leads to simple data structuren and communication patterns between blocks . Nevertheless, when geometrical boundaries (e .g. fault surfaces) become complex, multiblock grid with matched grids tends to create many blocks with small cells . We generalize the multiblock grid to the case where the gridlines do not match at block boundaries . The general quality and characteristics of multiblock grids, with matched or unmatched grids at the block boundaries, are discussed .Minti-point discretization scheures are necessary to accommodate non-orthogonal grid and tensor permeability . A flux-continuous finite difference scheme, which was previously developed for hexahedral grids with tensor permeability, is extended to multiblock systems with unmatched grids . We also present efficient iterative solution scheures that take advantage of the locally structured character of the computational grid .We demonstrate the capabilities of this generalized multiblock approach using examples of practical interest : (1) An SPE comparative study and (2) a real reservoir model with multiple complex faults and internal surfaces .