Abstract: It is a complicated and indescribed behavior of vibration waves propagating in non uniform beams. But the property of wave propagation can be expressed through calculation of transmission coefficients matrix and reflection coefficients matrix between arbitrary two cross sections on beams and a computation method is presented. The expression of power flow within propagation waves is also given in an application and it is used to calculate the transmission and reflection coefficient of power flow in non uniform beams. The numerical results show the non uniform extent of beams has more effects on power flow and the arrangement of beams has less, and it also demonstrates the good convergence and accuracy of this method.