A mathematical model has been developed for the mechanics of the cochlea that includes the effects of viscosity, the three-dimensional motion of the cochlear fluid, and the solid mechanics of the basilar membrane. Beginning with basic hydrodynamic equations for an incompressible viscous fluid, and through the use of a Green's function with two source points, an integral equation relating the pressure difference across the membrane to the motions of the stapes and membrance is derived. Another equation relating the membrane motion and pressure difference across it is obtained from basilar membrane solid mechanics. Combining these equations, a second-order differential equation is obtained which with its boundary conditions describes the pressure difference and thence membrane motion as a function of stapedial motion. Amplitude of the basilar membrane displacement, its maxima, locations of its maxima, and impulse propagation time along the membrane computed from the model are found in rough agreement with measurements of Békésy, Johnstone et al., and Rhode. Phase characteristics have features that are similar to those obtained from Moss-bauer measurements, cochlear microphonics and auditory nerve fiber responses. [Supported by N1H Grant RR 00396.]