Mammalian hearing relies on several complicated processes for successful sound detection including mechanotransduction of traveling waves within the cochlea. Linear math models can be used to predict basic cochlear mechanics; however, many significant nonlinearities exist in the traveling wave and have not been explained. Experimentalists now point to outer hair cell activity as the primary source of these nonlinearities. In this work a mathematical model of cochlear biomechanics is developed to describe the inner ear's nonlinear behavior. Coupled equations of motion for the fluid pressure and the basilar membrane displacement are utilized in conjunction with a formulated model for outer hair cell electromotility. Asymptotic methods are used to reduce the complexity of the problem, and a hybrid analytic-numeric method is used to approximately solve for the nonlinear waves.