The standard 2-dimensional cochlea model consists of a one-dimensional elastic structure which models the basilar membrane (BM) surrounded by an incompressible 2-dimensional fluid within the cochlear cavity. First we describe an idealized model in which the basilar membrane is modeled as an infinite array of oscillators and the fluid is described by Laplace's equation. In this idealized setting we show that the coupled system is approximately controllable with control acting on an arbitrary open set of the basilar membrane. If the basilar membrane has longitudinal membrane (string) elasticity, then exact controllability can be proved. Related results for similar fluid elastic systems are described.