Abstract: This paper investigates the stability of pipes conveying fluid on elastic foundation. The governing equations of the pipes are derived. Based on the initial parameter method, a concise relation between displacement vector and force vector at both ends of the pipe is obtained. For a pipe conveying fluid with arbitrary intermediate spring supports, a transfer matrix method is used to determine the characteristic equation, from which the critical velocity is calculated. Several numerical examples show that the present method may save computer time and achieve good accuracy since the characteristic equation is a two-order one. The influence of rigidity coefficient of the foundation on the critical velocity is discussed in detail.