Abstract: The dynamics of the axially moving beam has wide application in engineering, such as robot manipulators, machine tools and gun barrel, et al. Computing the dynamic response of axially moving beam is an important method to evaluate the dynamic performance and finally the structure design. The time-varying motion equations of the axially moving cantilever beam are derived using the Rayleigh-Ritz method and Lagrange's equation. The power series function is used to construct the trial function to solve the dynamic problem. Due to the good integral and differential performance of power series function, the derivation is easy to be carried out in the form of matrix. In this way, the symbolic computation software can generate the MATLAB program directly. And the generated MATLAB program can be used to conduct the dynamic computation with few modifications, because the basic data unit of MATLAB is matrix. The overall process is efficiency and the time from dynamic modeling to computation is greatly reduced. Through four sets of numerical examples, the computational accuracy of the presented method is validated by comparing the dynamic responses with those from previous literatures. Then, the effects of fitting order of the power series function on computational accuracy are discussed. And the principle to select the fitting order of the power series function to achieve good convergence and computational accuracy is given. Based on the dynamic model, the effects of axial motion frequency on transverse vibration are studied. The effects of axial vibration amplitude on the frequency response characteristic are explored. And the difference between considering gravity and neglecting gravity effect are compared.