The dynamic model of an extensible curved pipe with arbitrary initial configuration on elastic foundation was established in an arc coordinate system.Differential quadrature method(DQM)and partitioned matrix method were employed to obtain the natural frequencies and critical velocities of the pipe conveying fluid.The influences of elastic foundation and initial configuration on the dynamic stability of the pipe conveying fluid were discussed in detail.The numerical results show that the elastic foundation will increase the critical velocity of the pipe conveying fluid, and a small defect of the straight pipe will lead to a major effect on the critical velocity.