We worked to establish relationships among porosity, permeability, resistivity, and elastic wave velocity of diagenetically altered sandstone. Many such relationships are documented in the literature; however, they do not consider diagenetic effects. Combining theoretical models with laboratory measured data, we derived mathematical relationships for porosity permeability, porosity velocity, porosity resistivity, permeability velocity, velocity resistivity, and resistivity permeability in diagenetically altered sandstone. The effects of clay and cementation were evaluated using introduced coefficients in these relationships. We found that clean sandstone could be modeled with Kozeny’s relation; however, this relationship broke down for clay-bearing and diagenetically altered sandstone. Porosity is the first-order parameter that affects permeability, electrical, and elastic properties; clay and cement cause secondary effects on these properties. Rock physics modeling results revealed that cementation had a greater effect on elastic properties than electrical properties and clay had a larger effect on electrical properties than elastic properties. The relationships we provided can greatly help to determine permeability, resistivity, and velocity from porosity and to estimate permeability from resistivity and velocity as well as to determine resistivity from velocity measurements.