Several deficiencies affecting previous "box" models of the cochlea are overcome in this paper. Both mechanical and hydrodynamical aspects are treated at a level adequate to the complexity of realistic cochlear structures. The dynamics of the cochlea as a passive physical system, in the linear approximation, is described by an integral equation. It is further shown that this equation describes the properties of the working cochlea, provided a force term that accounts for hair cell motility is included. Numerical solutions for different degrees of outer hair cells activity, obtained by matrix methods in the frequency domain, are presented. Amplitudes and phases of the computer-simulated traveling waves are in fair agreement with basilar membrane responses to tones measured in various experimental conditions.