Present study examines the detonation wave propagation characteristics in annular channels. Numerical approaches used in the previous studies were extended with marching windows technique. Parametric study has been carried out using a radius of curvature normalized by the channel width considered as unique geometric parameter. In the channels of small radius of curvature, detonation wave is unstable and the regular cell structure is not observed. There is a critical radius of curvature where cell structure can be sustained. The effect of curvature makes the pressure difference on inner and outer surfaces where the detonation wave is overdriven. The results converge to that of straight channel as the radius of curvature gets larger, as expected.