The free vibration and the effect of material damping on damping factors are analyzed. An improved shell theory with shear deformation and rotatory inertia has been used, together with a semi-analytical higher order sub-parametric finite element with five nodes per element and 25 degrees of freedom. The convergence of the frequencies and damping factors for a simply supported shell is very fast; with one element the values converge to a practically acceptable limit. The damping factors associated with each mode of vibration are obtained by using a complex modulus for the material. The effects of various geometric properties on the vibration and the damping factors of circular cylindrical shells is studied. The effects of the mass distribution on natural frequencies and damping factors of the shells are also studied. It is found that the effect of mass distribution increases the damping factors of simply supported shells and decreases that of clamped-clamped shells. © 1994 Academic Press Limited.