The outer hair cell (OHC) is known to be the main source of nonlinear activity in the cochlea. In this work, we used a one-dimensional fluid model of the cochlea coupled to a nonlinear model of the mechanical to electric coupling of the OHC and the basilar membrane (BM). The nonlinearity arises from the electromotility and the voltage-dependent stiffness of the OHC, and from the displacement dependence of the conductance of the stereocilia. We used a reciprocal nonlinear piezoelectric model of the OHC in combination with a model of stereocilia conductance depending on BM displacement (which resulted in a nonlinear circuit model). The mechanical properties of the various components of the model were motivated from physiological components of the cochlea. Simulations showed realistic gains in the activity, response saturation at high force level, and two-tone forcing generated distortion products while the shape of the filtering function was not as accurately replicated. We conclude that a cochlear model with a simple 1D fluid representation in combination with nonlinear OHC-stereocilia electromechanical response characteristic qualitatively predicts the compression property of the cochlea and can be used as a tool to investigate the relative importance of the various nonlinearities.