Photoelastic modulator (PEM) is a kind of light modulator widely used in optical detection, which uses inverse piezoelectric effect of piezoelectric crystal to periodically change refractive index inside photoelastic crystal to realize phase modulation of optical signal passing through photoelastic crystal. PEM has the highest modulation efficiency when the system is in a resonant state. Therefore, resonant frequency and quality factor representing its working efficiency, are two important parameters of PEM. To study the resonance characteristics of PEM, we design a two-dimensional octagonal symmetric structure PEM with target frequency near 50 kHz and verify it theoretically and experimentally. At the same time, we propose a PEM resonance characteristic measurement method based on impedance analysis. In this paper, the theoretical parameters of the target PEM are obtained by establishing a frequency model for analysis, and then theoretical verification is carried out by numerical simulation software. Finally, two groups of PEM samples are prepared. In addition, the resonance characteristics of the samples are experimentally verified based on the impedance analysis method. The measured resonant frequencies of the sample PEMs are 52.363 kHz and 52.353 kHz, and the quality factors are 5071.2 and 6096.7, respectively.