In this work certain results has been presented of an analysis of the influence of material damping on changes in the propagation of elastic waves in beams. A new and original method has been proposed for formulating the dynamic stiffness matrix for a beam spectral finite element. This new approach enables one to enhance the proposed element by including terms previously ignored likes material damping or initial stresses. Numerical examples presented illustrate the influence of damping intensity on the range of propagating waves, as well as the dispersion effects due to the damping.