The characteristics of the beam-mode stability of the fluid-conveying shell systems are investigated in this paper, under the clamped-clamped condition. A finite element model algorithm is developed to conduct the investigation. A periodic structure of functionally graded material (FGM) for the shell system, termed as PFGM shell here, is designed to enhance the stability for the shell systems, and to eliminate the stress concentration problems that exist in periodic structures. Results show that (i) the dynamical behaviors, either the divergence or the coupled-mode flutter, are all improved in such a periodic shell system; (ii) the critical velocities u _cr for the divergent form of instability is independent of the normalized fluid density β; (iii) various critical values of β exist in the system, for indentifying the coupled modes of flutter (Païdoussis-type or Hamiltonian Hopf bifurcation flutter) and for determining the mode exchange; (iv) changes of some key parameters, e.g., lengths of segments and/or ‘grading profiles’ could result in appreciable improvement on the stability of the system.