The coupled fluid-structure interaction problem is analyzed using the theoretical method to investigate the critical fluid velocity of cantilevered cylindrical shells conveying an incompressible, inviscid fluid. The cantilevered cylindrical shell has an intermediate support at the arbitrary axial position. The intermediate support condition can be modeled by two types of springs: the translational spring and rotational spring. The springs are continuously and uniformly distributed along the circumferential direction. The steady flow of fluid is described by the classical potential flow theory. The motion of shell is represented by the first order shear deformation theory (FSDT) to account for rotary inertia and transverse shear strains. The effect of internal fluid can be taken into consideration by imposing a relation between the fluid pressure and the radial displacement of the structure at the interface. Numerical examples are presented and compared with exiting results.