This paper presents a free vibration analysis of thick cantilevered arbitrary triangular plates based on the Mindlin shear deformation theory. The solutions are computed using the recently developed pb-2 Rayleigh-Ritz method. The actual triangular plate is first mapped onto a basic square plate, and the deflections and rotations of the plate are approximated by Ritz functions defined as products of two-dimensional polynomials in the basic square plate domain and a basic function. The basic function satisfies the geometric boundary conditions at the outset and is chosen as the boundary expression of the cantilevered edge. Stiffness and mass matrices are integrated numerically over the domain of the basic square plate using Gaussian quadrature. Wherever possible, the present results are verified by comparison with existing analytical and experimental values from the open literature. To the authors' knowledge, first known results of natural frequencies for cantilevered arbitrary triangular Mindlin plates are presented for a wide range of geometries and thicknesses. These results are valuable to design engineers for checking their natural frequency calculations and may also serve as benchmark values for future numerical techniques and software packages for thick plate analysis. The influence of shear deformation and rotary inertia on the natural frequency parameters are examined.