In the present study, effect of satisfying stress boundary conditions, in addition to displacement boundary conditions, in the axisymmetric vibration analysis of circular and annular plates is investigated. A new axisymmetric finite element, which is based on a combination of the conventional displacement-type variational principle and the Reissner¡¦s principle, is proposed. With this formulation, stresses, like displacements, are primary variables, and both displacement and stress boundary conditions can be easily and exactly imposed. Axisymmetric vibration frequencies of some typical circular and annular plates are then obtained with the present approach and are compared with those by the displacement-type axisymmetric finite element. It is found that the conventional finite element, though not satisfying stress boundary conditions, can still obtain sufficiently accurate vibration frequencies of circular and annular plates.