Abstract Previous research into structural vibration transmission paths has shown that it is possible to predict vibrational power transmission in simple beam and plate structures. However, in many practical structures transmission paths are composed of more complex curved elements; therefore, there is a need to extend vibrational power transmission analyses to this class of structure. In this paper, expressions are derived which describe the vibrational power transmission due to flexural, extensional and shear types of travelling wave in a curved beam which has a constant radius of curvature. By assuming sinusoidal wave motion, expressions are developed which relate the time-averaged power transmission to the travelling wave amplitudes. The results of numerical studies are presented which show the effects upon power transmission along a curved beam of: (i) the degree of curvature; and (ii) various simplifying assumptions made concerning beam deformation.