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Rocks generally have a percolation porosity at which they lose rigidity and fall apart. Percolation behavior is a purely geometrical property, independent of any physical properties, and is a powerful constraint on any valid velocity-porosity relation. We show how the conventional Differential Effective Medium (DEM) theory can be modified to incorporate percolation of elastic moduli in rocks by taking the material at the critical porosity as one of the constituents of a two-phase composite. Any desired percolation porosity can be specified as an input. In contrast, the conventional DEM model always predicts percolation at a porosity of either 0 or 100 percent. Most sedimentary rocks however have intermediate percolation porosities and are therefore not well represented by the conventional theory. The modified DEM model incorporates percolation behavior, and at the same time is always consistent with the Hashin-Shtrikman bounds. The predictions compare favorably with laboratory sandstone data.