The methods currently used for computation of resonant frequencies of a microwave dielectric resonator all require knowledge of the field structures, both inside and outside the resonator, and therefore are strictly limited. The paper discusses the general principle of solution of resonant frequencies of the dielectric resonator by the boundary element method (BEM). Through discretisation, the boundary integral equations are reduced to a generalised eigenvalue equation, with the eigenvalues as the resonant frequencies. The method presented is, in principle, applicable to an arbitrarily shaped dielectric resonator. Some results are given and compared with previous data published as a demonstration of the validity of the method.