An approach of calculating the coupling losses in a coaxial (or annular) waveguide laser resonator is developed by which the computational time is considerably reduced. Computations of the coupling losses for some TE modes of an annular waveguide, as a function of mirror curvature and position, are presented in the limit of large mirror aperture. It is shown that there exist three special configurations to provide low coupling losses. The resonator properties are discussed. The calculating results are useful for design of annular waveguide laser resonators.