Brillouin scattering has been used to probe the acoustic phonons of the monoclinic (P2(1)/c) polymorph of the drug carbamazepine (CBZ III). By sampling a variety of acoustic phonons, the complete elastic constant tensor has been determined for this CBZ polymorph. The diagonal elastic constants C-11, C-22, C-33, C-44, C-55 and C-66 are 10.89, 11.47, 11.32, 3.68, 0.85 and 2.89 GPa, respectively. The elastic constants of CBZ III are effectively governed by nondirected dispersive type interactions similar to aromatic systems with delocalized pi bonds. The bulk modulus and linear compressibility have been calculated from the compliance matrix. The relative strength of intermolecular interactions in different directions is estimated from the linear compressibility plotted in three crystallographic planes. Cauchy's ratio, calculated from the elastic constants, suggests that many-body forces of dispersive interactions contribute significantly to the lattice anharmonicity of CBZ III.