Employing polyhedral specimens, longitudinal and shear wave velocities were measured in various directions of propagation and polarization. Sound velocities showed orthorhombic elasticity in all of the rocks. With the assumption of orthorhombic elasticity the nine stiffness constants of all samples were determined by the sound velocities under atmospheric pressure and Kelvin-Christoffel's equation. Twenty-one stiffness constants of Oshima granite, determined without assuming any symmetry, also showed orthorhombic features. Directions of the symmetry axes agreed well with the orientation of the preexisting cracks. Akaike's Information Criterion showed that the orthorhombic model with nine nonzero elastic stiffnesses was better than the model having 21 nonzero elastic stiffness for Oshima granite. The polyhedrons of two granitic rocks were loaded under hydrostatic pressure. All components of the stiffness constants increased with pressure. Under pressure of more than 120 MPa, two granitic rocks were approximately isotropic. The results show that oriented microcracks are mainly responsible for the orthorhombic elasticity of the granitic rocks and also indicate that dry oriented cracks can not be a cause for the anisotropic elasticity of granites at depths of more than 6--8 km. ¿ American Geophysical Union 1992