Acoustic resonant transmission (RT) phenomenon found in Bragg couplers made of alternatively high (H) and low (L) impedance materials is theoretically investigated. The existence of the RT within the Bragg stop bands is analytically demonstrated, along with the exact peak values expressed in closed form in terms of the coupler parameters. RT takes place either when the coupler is terminated with an L-layer and has its bottom surface free, or when it is terminated with an H-layer and the bottom clamped. Numerical results are given for the transmission and reflection rates in Bragg couplers made of tungsten and SiO2 layers.