Blot showed that elastic waves could be guided by a cylindrical hole in a homogeneous isotropic elastic solid. This problem is generalized to materials with cylindrical orthotropy, this being a plausible model for waves in wood. For time-harmonic motions, the problem is reduced to some coupled ordinary differential equations. Methods for solving these equations are discussed. These include the method of Frobenius (power-series expansions) and the use of asymptotic expansions (valid far from the cylindrical hole).