The use of ultrasound for determining the elastic constants of materials is a well-established science for homogeneous materials such as metals. However, its extension to anisotropic, inhomogeneous materials such as wood has proved more problematic. Wood is modelled as an orthorhombic material with the influence of inhomogeneities generally being neglected. For this paper the potential influence of inhomogeneities on waves propagating in the radial direction was considered. Within ring density and ultrasonic velocity measurements were made. A model for ultrasound propagation in the radial direction was then constructed which treats the annual ring structure in the radial direction as a layered structure and predicts the occurrence of stop bands in the frequency domain. Evidence for the existence of such stop bands is considered.