A method of analysis is presented to determine the free vibration frequencies of plates having corner stress singularities. Displacements are assumed in the form of polynomials, and corner functions are added which yield the desired stress singularities where needed (i.e., in sharp interior corners). Frequencies are determined by means of the Ritz method. The importance of using corner functions is demonstrated by means of convergence tables. Numerical results are presented for cantilever skew (parallelogram) plates and for circular plates with V-notches.