The invention relates to a theory and a design method of a silencer with a circular cavity and belongs to the field of distributed energy resource noise reduction. According to the design method of the silencer with the circular cavity, a reasonable design size of the silencer with the circular cavity is obtained by means of relationships among flue gas flows, air leakage factors, Cauchy factors and noise reduction amount and moving characteristics of fluid dynamics. The noise reduction amount in a low frequency phase is larger than or equal to 10dB, and when the frequency is larger than 1000Hz, the noise reduction amount can reach 34dB. The design method of the silencer with the circular cavity is particularly suitable for noise control with different center frequencies and design of large noise elimination and reasonable. At the same time, the design method of the silencer with the circular cavity is not limited in the silencer with the circular cavity, but also suitable for design of a boiler smoke outlet silencer.