In this paper, we report the optimal design of a support for a fundamental-type plano-convex AT-cut quartz resonator which was fabricated using our newly developed etching process. We established a three-dimensional finite element model and carried out eigen-frequency analysis. To describe quantitatively the energy trapping performance of the resonator, we introduced a parameter called the energy trapping rate, which is defined by the ratios of the vibration energy inside to that outside of the electrode region. Two types of our newly designs were evaluated in this work, and the optimal one providing large energy trapping rate was determined. Based on the calculated results, we fabricated resonators and measured their Q-factors. The calculation and experiment results show an improvement in the efficiency of resonator performance. High Q-factors were also obtained.