The natural frequencies of twisted cantilevered parallelepipeds are determined using the Ritz method. Assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly, and which are mathematically complete. Reasonably accurate nondimensional frequencies are calculated for low aspect ratio, thick and thin parallelepipeds having arbitrary degrees of initial twist. Detailed numerical studies show that a three-dimensional analysis is essential in monitoring coupled flapwise-sideways bending, coupled thickness-shear-bending, coupled thickness-twist-bending, and torsional sensitivities in the variation of nondimensional frequencies with increasing twist angles and decreasing thickness ratio ranging from the limits of classical thin-plates to very thick parallelepipeds. Results obtained using the present method are compared with those obtained in a detailed three-dimensional finite element study, where the suitability and limitations of h-version solid element discretizations are discussed.