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To develop millimeter-wave modulators, high-anisotropy uniaxial monocrystalline hexagonal ferrite resonators (HFRs) can be used. One of the ways to modulate the hexagonal ferrite resonator's resonance frequency is to periodically vary the angle between the equilibrium magnetic moment and the external magnetization field. This angular control can be exercised by the mechanical (acoustic) oscillations excited in a piezoelectric slab having a good acoustic contact with the HFR. We consider a quasi-static mathematical model of the uniaxial HFR with the angular control of its resonance frequency. We analyze the amplitudes of harmonics of the modulated millimeter-wave signal, and we derive the optimal orientation of the ferrite crystallographic axis. We suggest some ideas regarding the design of a modulator on the basis of an HFR and a piezoelectric slab, and we present experimental results.