The effect of axial deformation of shell particles on the dynamic instability (flutter) of cantilevered cylindrical shells made of functionally graded materials (FGM) under an end axial follower force is addressed. To this end, at first, results for free vibration of FGM cylindrical shells were verified with previous outcomes and they were in very good agreement. Then, the effect of axial deformation of the shell, acting like a reducing linearly-distributed follower load, on the critical circumferential mode number and the flutter load of FGM shells was accounted for. Finally, the effect of axial deformation of the shell particles on the critical circumferential mode number and the flutter load of FGM shells were investigated. In this case, three homogeneous shells with different elasticity moduli and densities and two FGM materials were considered: nickel-stainless steel and stainless steel-alumina. Results include the increasing critical circumferential mode number and the increasing value of the flutter load due to axial deformation. The increase in the flutter load occurs in proportion to the whole elasticity modulus of the material, and thus it can be derived from the formula of mixture for an FGM.