Consideration is given in this paper to the problem of a thick, spinning, annular disk constrained at its inner radius. Mindlin’s transverse shear deformation and rotary inertia terms are included in the eigenvalue formulation. In the modified Rayleigh–Ritz method used here, the ‘‘admissible’’ or ‘‘trial functions’’ are developed numerically by an iterative scheme so that all the forced, as well as natural, boundary conditions are fully satisfied. The natural frequencies for different mode shapes of the disk have been computed and are presented in a nondimensional form as a function of rotating speed.