Abstract: The differential quadrature method (DQM) is an efficient numerical one to solve the boundary/initial value problems because of its mathematical simplicity, decreased amount of computation, easy programming and high precision. The method is extended to the stability analysis of elastically-supported fluid conveying pipelines. The numerical computation results showed that DQM has a unique merit to the dynamic analysis of the characteristics of the fluid conveying pipelines concerning with the fluid structures interaction (FSI). Discusses the stability of such pipelines under common end constraining conditions and the effects of both torque spring and linear spring coefficients on the pipelines' stability. Some preliminary conclusions are thus drawn involving the design of such pipelines and relevant reliability analysis, which are available for technological reference.