This paper treats the transmission of the vibrational waves through a beam with many appendages. The conclusions are as follows. 1. When beam system has many appendages which may have couplings between flexural and longitudinal waves, the amplitudes of flexural waves (progressive and near field waves) and longitudinal waves (progressive waves only) of adjacent beam elements both sides of an appendage can be related with matrix. So the amplitudes of both extreme ends can be connected by the products of matrices when the appendages, which must not necessarily be same property, are attached in arbitrary distances. 2. In the analysis of flexural wave transmission problems, matrix mentioned above can be simplified in the relation of progressive flexural waves only when masses, which have no coupling properties, are installed in larger distances in comparison with wave lengths. 3. The transmission waves can't always be attenuated even if another new masses were fitted. The ratio of amplitudes of adjacent beam elements can't be determined locally but the boundary conditions of whole system must be considered. 4. The idea that the magnitudes of transmission energy are expressed by the amplitudes of progressive and near field waves clarifies the mistake of “propagation constant” mentioned in other literatures. 5. To check the above theory, the bending wave propagation on a beam with lumped masses was measured. In general, the theory and the experiments were fairly in good agreemant.