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Micromechanical resonators are miniature devices that vibrate at high frequencies. Nowadays, with the recent advances in micro-electro-mechanical systems (MEMS) fabrication technology, micromechanical resonators are used widely in sensors, wireless communication and navigation systems. The commonly encountered energy loss mechanisms in micromechanical resonators include air damping, thermoelastic dissipation and anchor loss. In this paper, with regard to the dominated quality factor by anchor loss in some important applications including oscillators, electrical filters and gyroscopes, the closed-form expression is obtained for anchor loss quality factor in the plunging-mode vibrations of micromechanical rectangular-plate resonator with two support beams. The findings are validated by comparing with experimental data. As far as there is an acceptable match between the analytical and experimental results, the proposed model is confirmed. The results also show that the anchor loss quality factor increases with increasing substrate thickness. Moreover, a new design is proposed to enhance the anchor loss quality factor in the plunging-mode vibrations of micromechanical rectangular-plate resonators. For this purpose, the conventional support beams are replaced with T-shaped support beams. Besides, the results show that the anchor loss quality factor at the same resonant frequency is enhanced about 1.5 times.