The paper presents an application of the boundary element method (BEM) to the calculation of the resonant frequencies of a cavity resonator. A three-dimensional vector boundary integral equation suitable for the cavity resonator problem is first given and then discretised resulting in a generalised eigenvalue equation with resonant frequencies as its eigenvalues. The method is applicable to an arbitrarily shaped cavity and the numerical computation is easy to carry out. To demonstrate the accuracy and the feasibility of the method, several numerical examples are presented.