Abstract: The interaction between the pipeline and soil during earthquake may cause the pipeline deformation, result in stress in pipeline and affect the pipeline safety. Considering the differential equations of the longitudinal vibration of underground pipeline under the effect of earthquake * this paper selects the tri-angle functions as trial functions to satisfy the boundary and initial conditions. Using the method of weighted residuals computes the longitudinal reaction of pipeline to earthquake. It may compute the strain and stress in pipeline, then determine the strength of pipeline. One computation example shows that the method can effectively compute the longitudinal vibration of underground pipeline under the effect of earthquake. It may be useful to the anti-earthquake design for underground pipeline.