A porous granular rock is modeled by an aggregate of identical, randomly stacked, spherical particles. Contacting particles are initially bonded together across small areas. A theory is developed for the deformation of two such spherical particles under equal and opposite forces acting through the line joining their centers. The theory is used to calculate the effective elastic moduli of the medium. The dependence of the derived elastic wave speeds on the confining pressure and adhesion radius of the contacting particles is then predicted.