The resonance characteristics of a three-dimensional anisotropic metamaterial bilayer is investigated through solving the resonance equation for a rectangular cavity filled with two layers of different isotropic metamaterials. It is found that the solution of subwavelength resonance is highly dependent on the product of the transversal and longitudinal permeabilities，and there exist more than one for the subwavelength resonance in most cases. In addition，it is found that the width of the corresponding waveguide of the rectangular cavity has an essential effect on the number of solutions for the resonance condition equation. These results are of significance in the application of the metamaterials to sub-wavelength resonance structures and miniaturized cavity resonators.