A new method for the determination of finely-gridded reservoir simulation pressures has been developed. It is estimated to be as much as hundreds to thousands of times faster than other methods for very large reservoir simulation grids. The method extends the work of Weber et al. Weber demonstrated accuracies for the pressure solution normally requiring millions of cells using traditional finite-difference equations with only hundreds of cells. This was accomplished through the use of finite-difference equations that incorporate the physics of the flow. Although these coarse-grid solutions achieve accuracies normally requiring orders of magnitude more resolution, their coarse resolution does not resolve local pressure variations resulting from fine-grid permeability variations. Many oil reservoir simulation models require fine grids to adequately represent the reservoir properties. Weber's coarse grids are of little value. This study takes advantage of the accurate coarse-grid solutions of Weber, by nesting them in the requisite fine grids to achieve much faster solutions of the large systems. Application of the nested-grid method involved calculating an accurate solution on a coarse grid, nesting the coarse-grid solution as fixed points into a finer grid and solving. Best results were obtained when an optimal number of coarse-grid pressure points were nested into the fine grid and when an optimal number of nested-grid systems were used.