The Ritz method Is applied In a three-dimensional (3-D) analysis to obtain accurate frequencies for thick. linearly tapered. annular plates. The method is formulated for annular plates haying any combination of free or fixed boundaries at both Inner and outer edges. Admissible functions for the three displacement components are chosen as trigonometric functions in the circumferential co-ordinate. and a1gebraic polynomials in the radial and thickness co-ordinates. Upper bound convergence of the non-dimensional frequencies to the exact values within at least four significant figures is demonstrated. Comparisons of results for annular plates with linearly varying thickness are made with ones obtained by others using 2-D classical thin place theory. Extensive and accurate ( four significant figures ) frequencies are presented 7or completely free. thick, linearly tapered annular plates haying ratios of average place thickness to difference between outer radius (a) and inner radius (b) radios (h$_{m}$/L) of 0.1 and 0.2 for b/L=0.2 and 0.5. All 3-D modes are included in the analyses : e.g., flexural, thickness-shear. In-plane stretching, and torsional. Because frequency data liven is exact 7o aulcorner least four digits. It is benchmark data against which the results from other methods (e.g.. 2-D 7hick plate theory, finite element methods. finite difference methods) and may be compared. Throughout this work, Poisson`s ratio $upsilon$ is fixed at 0.3 for numerical calculations.s.