Many previous studies on characteristics of thermoacoustic regenerator are based on fluid micro-groups and their compression–expansion cycle. In this paper, coincident frequency is introduced to evaluate its acoustic characteristics by combining structural acoustic with structural vibration theories. The relationship among structure wave radiation and regenerator position, slab thickness, and properties of material are analyzed by numerical calculation. The results show that in the low-frequency thermoacoustic system, the coincident effect generated by higher frequency wave weakens the fundamental sound wave. While in the high-frequency thermoacoustic system, where the oscillating fundamental frequency is higher than the coincident frequency, the sound field strength is enhanced by stronger structure wave radiation because of the coincident effect.