The natural frequencies of inplane vibrations of polar orthotropic annular plates with linearly varying thickness have been analysed. A semi-analytical method of analysis has been used where the radial and tangential displacements are expanded in the circumferential direction as Fourier series and the radial behaviour is solved using the finite element method. For the sake of comparison, results have been obtained starting with two different kinds of displacement functions. The frequencies have been studied with respect to various boundary conditions. aspect ratios, thickness ratios, ratios of moduli, and two fibre directions. © 1988.