Methods of solution are given for the sonic resonances corresponding to the free flexural and torsional vibrations of an anisotropic bar of rectangular cross section. The resonance equations for the torsional vibrations of a symmetric, three‐piece, cylindrical compound oscillator are derived. The particular application of the methods and equations for the determination of some of the elastic constants of compression‐annealed pyrolytic graphite, a highly anisotropic material, is discussed.