This paper investigates asymmetric vibrations of non-homogeneous circular plates of parabolically varying thickness on the basis of classical plate theory. The non-homogeneity of the plate material is assumed to arise due to exponential variation in Young’s modulus as well as density along radial direction in distinct manner. First three natural frequencies of clamped, simply supported and free plates have been obtained using Ritz method. The basis functions have been chosen as polynomial co-ordinate functions satisfying the essential boundary conditions. Thereafter, the effects of taper parameter, non-homogeneity parameter, density parameter and nodal diameter have been analysed for first three modes of vibration. The results obtained are compared with those available in literature for homogeneous and non-homogeneous plates.