Abstract: In this paper,a combination of integral and differential methods were applied to calculate the mode characteristics of beamconvereting annular resonator with various chemical annular gain medium.Two designs were compared:one is designed without beam rotaion in the compact leg,and the other with beam rotating 90°. It shows that beam rotation in the compact leg has little effect on the mode characteristics,when the resonator is aligned perfectly.However,when the resonator is misaligned,beam rotation in the compact leg can not only sustain zerolevel mode, but also get better beam quality and output power than the resonator without beam rotation. In practice resonators can not be aligned perfectly,so beam rotation is necessary to beamconverting annular resonator.