Abstract: In this paper, underground pipeline is modeled as a beam on elastic foundation. The differential equation of vibration is established,and then the boundary conditions are properly treated. Analytic solutions of pseudo-static displacements,dynamic displacements and internal forces for bending vibration are derived in series expansions. Thus the usual method for the discretized system under the action of multi-support excitations is expanded and can be applied for the continuous system. The calculation in the example shows that the results are satisfactorily met.