Harmonic lattice dynamical calculations in the rigid-body approximation are employed to probe elastic and dynamic properties of the alpha-phenazine molecular crystal. The intermolecular interaction for an optimized lattice structure is defined by the Buckingham potential. The velocities of the acoustic phonons obtained from dispersion curves of normal modes in the region of the Brillouin zone center allow evaluation of the full set of elastic constants. Modeling of the homogeneous deformation of the crystal lattice is used to obtain frequency changes of the optic modes, which yield estimates for the anisotropic mode Gruneisen parameters. Relaxation of the internal strains is employed for a realistic modeling of the crystal response to the external strains and stresses. The anharmonicity and anisotropy of the intermolecular interactions are assessed from the derived parameters.