A hydrodynamical theory is given for a model of the cochlea. The model consists of two channels of varying but equal cross sections. The channels are separated by an elastic membrane with variable dynamical constants. The two channels are interconnected at one end, and the entire structure is rigidly enclosed except for two accessible areas corresponding to the round and oval windows. The equations of motion, continuity including the effect of the membrane, and appropriate boundary conditions are formulated. As a first step toward a complete analysis the non‐dissipative case is considered. Numerical solutions are found using experimental data obtained by G. v. Békésy. Localization phenomena and phase velocities are found to be in broad agreement with experimental data.