Beam-converting annular resonator (BCAR) possesses outstanding characteristics of high extraction efficiency and near-diffractive beam quality. It is applied specially to annular HF/DF gain medium. A finit difference method is used to calculate the modes of BCAR with various active medium. It showed that BCAR is insensitive to aberrations introduced by active medium, the optical quality is excellent, and extraction efficiency of BCAR is high under all the conditions. When a shock wave exists in the active medium, Strehl ratio of BCAR can still reach 0.899, the intensity distribution on cavity mirrors is reasonable, thus the damage possibility resulting from thermal load on the mirrors is lower than the usual unstable resonators. All above advantages make BCAR a very useful resonator applied not only to high energy chemical lasers but also to other high energy lasers with annular gain medium.