The natural frequencies of inplane vibration of polar orthotropic annular plates with parabolically varying thickness have been analysed. In the semianalytical method used, the radial and tangential displacements are expanded in the circumferential direction as a Fourier series and the radial behaviour is modelled by finite elements. Since published results were not available, results were obtained using tow different kinds of displacement functions. The frequencies have been studied with respect to various boundary conditions, aspect ratios, ratios of moduli, thickness ratios and for two orientations of the fibre directions. © 1989.