When attempting to control the vibration transmitted from a machine into and through the structure upon which it is mounted, it is desirable to be able to identify and quantify the vibration transmission paths in the structure. Knowledge of transmission path characteristics enables procedures to be carried out, for example, to reduce vibration levels at points remote from the source, perhaps with the objective of reducing unwanted radiation of sound. One method for obtaining transmission path information is to use the concept of vibrational power transmission. In any vibrating system there are a variety of mechanisms by which the vibration is transmitted through the substructure. The concept of power transmission allows the magnitude and direction of the various transmission paths to be compared. Simple measurements of vibration amplitude at various points in the structure do not suffice to identify the vibration paths. If stationary waves are present in the structure, large vibration amplitudes will be measured while power is being transmitted through the structure. Measurements are made of the vibrational power associated with flexural and longitudinal waves in beam-like structures carrying both wave types simultaneously. In order to make these measurements the relationship between measured wave amplitude and vibrational power is determined. Much care is taken in identifying the various sources of error in the measurements and the possible methods of eliminating these errors. Predictions are made of the vibrational power transmission in beams containing flexible sections and bent and branched beam systems. Models are developed which determine the wave type which carries most power in each section of the system. The theoretical predictions are confirmed by experimental observation. By establishing the wave type which predominantly causes power transmission it is then possible to apply the most suitable vibration control technique.