  We present here a study of the radial modes for infinitely long cylinders and
cylindrical shells of general anisotropic crystals. The elastic coefficients
matrix includes twenty-one independent constants. We obtain expressions in
closed form for the dispersion relation, valid for any anisotropic material. In
the case of the lowest breathing mode of a thin cylindrical shell we obtain a
simple analytical formula. This can be used to obtain a first estimate of the
breathing mode frequency in nanotubes for any material.
