In a recent companion paper, the efficacy of higher-order shear deformable, C0 continuous, Lagrangian isoparametric plate finite element analyses has been demonstrated on cantilevered skewed (parallelogram) thick plates. The present work extends the method to include skewed thick plates having trapezoidal and triangular planforms, and is the first known vibrational study of such plates. Extensive and accurate nondimensional frequency tables and graphical charts are presented for a series of trapezoidal plates showing the effect of aspect ratio, chord ratio, thickness ratio, and skew angle. The need for the present higher-order shear deformable plate finite element method for skewed trapezoidal plate vibrations increases as the skew angle increases and as the aspect ratio, chord ratio, and thickness ratio decreases. Some theoretical and experimental data hitherto published for delta and skewed triangular cantilevered plates are compared with results obtained using the present finite element method. No published theoretical results for cantilevered skewed trapezoidal and triangular thick plates are known to exist.