The human cochlea is very effective at discriminating sound waves at different frequencies, but is also notable for its complicated geometry and small physical size. This paper describes a elative simple representation of the cochlea that efficiently models wave propagation along it by incorporating fluid-structure coupling between the two fluid chambers and the inhomogeneous basilar membrane (BM) that separates them. The numerical solution is initially obtained by using the Finite Element (FE) method, by connecting a series of elements with longitudinal variation in Young's modulus. The wavenumbers of each section are then obtained by applying the Wave Finite Element (WFE) method and the Wentzel–Kramers–Brillouin (WKB) approximation is used to model the wave propagation. The WFE method provides a new and powerful way of predicting the important characteristics in the cochlea at low computational cost which is less than half in both time and of the memory requirement of a full FE model.