Abstract: In this article,the equations of motion for the cracked cantilevered pipe conveying fluid is derived based on the extended Lagrange equations for systems containing non-material volumes.The virtual work done by the discharged fluid and that done by the fluid at the crack position due to the geometrical dis-continuity conditions are considered in the present equations of motion.There are geometrical discontinuity conditions at the crack’s location.The mode functions which satisfy the boundary conditions and geometrical discontinuity conditions are obtained by adding polynomial functions to the modal functions of the uncracked beam.The lowest three frequencies are computed and compared with results of the model for the cracked cantilevered pipes conveying fluid in existence.That shows the present derivations are reasonable.The stability of the cracked cantilevered pipes conveying fluid is studied and the effects of the crack on the eigenvalue branches which flutter occurs in are depicted.