In this paper, an approximate analysis using a layerwise approach is presented to study the vibration of thick circular cylindrical shells on the basis of three-dimensional theory of elasticity. The boundary conditions studied are simply supported}simply supported and clamped}clamped boundary conditions. In this approach, the thick cylindrical shell is discretized into an arbitrary number of thin cylindrical layers in the thickness direction and each layer assumes a three-dimensional stress state. The approach is similar in concept to the "nite-strip method. The displacements for each layer are approximated by trigonometric functions in the axial and circumferential directions and by some linear-shape functions in the thickness direction. The governing equation is obtained using an energy minimization principle. Extensive frequency parameters, never seen in the literature before, have been presented for a wide range of thickness-to-radius ratios and thickness-to-length ratios. In addition, the frequency characteristics of thin and thick cylindrical shells are also studied and the displacement "elds in the thickness direction for various thickness-to-radius ratios are also presented. The analysis has been veri"ed by comparing results with those in the literature and excellent agreement is obtained.