A study is made of the dimensional resonances of the thickness modes of shear magnetoelastic and elastic (MEE) vibrations in a bilayered structure: magnetic-nonmagnetic dielectric. The efficiency of dimensional resonance excitation is considered. We show that the magnetic susceptibility of the thickness modes of shear MEE vibrations attains extreme values in the case when the position of an interface coincides with one half and one quarter of a MEE wavelength. The magnetic susceptibility calculated for the resonant frequencies changes in a nonmonotone way with the change of relative thickness of the magnetic layer. The form of nonmonotone regions depends on the relations between the elastic moduli of magnetic and nonmagnetic layers, the position of interface and differs for odd and even resonant frequency harmonics.