From the sound velocity measured using the Brillouin scattering technique, the elastic, piezoelectric, and dielectric constants of a high-quality monodomain tetragonal Rh:BaTiO3 single crystal are determined at room temperature. The elastic constants are in fairly good agreement with those of the BaTiO3 single crystal, measured previously by Brillouin scattering and the low-frequency equivalent circuit methods. However, their electromeehanical properties are significantly different. Based on the sound propagation equations and these results, the directional dependence of the compressional modulus and the shear modulus of Rh:BaTiO3 in the (010) plane is investigated. Some properties of sound propagation and electromechanical coupling in the crystal are discussed.