In the present paper, the exact vibration characteristics of multi-span pipe conveying fluid has been studied. A mathematical model and a computer program are used to obtain the results. Results of typical cases have been obtained using the current model and compared with the relevant published results. The effect of intermediate support location on the vibration characteristics of clamped-pinnedpinned pipe carrying concentrated masses is evaluated. Natural frequencies and the critical flow velocity of the selected pipe are determined for different locations of both the intermediate support and the concentrated masses. Nodal and anti-nodal points of the mode shape are investigated due to the change of the intermediate support location for accepted observability and controllability aspects.