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The propagation of circular Rayleigh waves generated by a pulsed laser line-source in cylinders is systematically studied in this dissertation.Firstly, the propagation of elastic waves in cylinders is theoretically studied. The dispersive properties of circular Rayleigh waves are then discussed in detail. The dispersive curves of phase velocity and group velocity are obtained for different materials and different diameters, respectively. These studies show that the dispersive property of the circular Rayleigh wave is not complicated. Its phase velocity cp and group velocity cg are both greater than the velocity of the plane Rayleigh wave cr and become less when the radius R increases. When R —> oo, cp and cg —> cR. While R decreases, both of cp and cg increase at first and may be greater than the shear wave velocity of the media. When R is very small, cp will arrive at its maximum in a certain radius Rs. cg = cp and no dispersion happens for Rs. When R < Rs and R —>0, cp will decrease and cg increase at first and then decrease, too. For a cylinder with a given radius, cp and cg both decrease and trend to cr if the frequency f increases. When f decreases, cp and cg will increase and arrive at their maximum at first and then decrease. These conclusions provide theoretical evidences for the application of circular Rayleigh waves in non-destructive evaluation （NDE） of the circular cylinder surface.Secondly, in a new attempt, the Finite Element Method （FEM） is used in simulating the propagation of elastic waves in cylinders. In order to simulate the problem in high frequency, a new sub-matrix method is set up for the large-scale computation of FEM. Codes of this method are developed. The displacement fields generated by a pulsed line-source in the crack-free and surface-cracked cylinders are computed, respectively. These displacement fields are displayed by color images, which give clear ideas on the propagation of the different wave types in cylinders. The color images of surface-cracked cylinders clearly display the influence of the crack. The A-scan results