Based on the mode-matching method, an analytical model with full-wave coupling is presented for the coaxial Bragg structures corrugated with rectangular ripples, where the expressions of the reflectivity and transmission rate for each involved mode are derived. The validity of the analytical model is examined in terms of a reported experiment, and good agreement between the theoretical results and the experimental measurements is demonstrated. Comparative study is carried out between the present model and the published theoretical results. It is found that the approximate treatment adopted by the previous model leads to notable deviation of the transmission response curve due to the neglect of the evanescent modes excited by rectangular ripples. The analytical method presented in this paper can be expected to provide a useful approach to the characteristic investigation and engineering practice of the coaxial Bragg structures with rectangular ripples.