This article presents the analysis of functionally graded hollow cylinders with finite length under axisymmetric dynamic loads. It is assumed that the functionally graded cylinder is comprised of metal-phase and ceramic-phase and material properties are graded in the thickness direction of the cylinder according to a power law distribution. The axisymmetric governing equations of motion are derived. To solve them, two dimensional finite element and Newmark’s methods are used. By this method, loading in longitudinal and radial directions can be applied as an arbitrary function of time and coordinates. In a simple case, an internal pressure which increases exponentially from zero to a final value is applied. Radial displacement for long time is obtained and compared to analytical result of an isotropic thick hollow cylinder under uniform internal pressure. In another case, internal pressure is applied as a triangular pulse and dynamic response is investigated. By using the fast Fourier transform (FFT), the time response is transferred to frequency domain and natural frequencies are illustrated. As another axisymmetric load, a radial line load which is uniformly distributed along circumferential direction is considered and longitudinal wave propagation through the length of the cylinder is illustrated. Also the mean velocities of wave propagation are obtained. Numerical results for thick cylinders and cylindrical shells are obtained and compared with the results for isotropic cylinders.

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