Cochlear implantation is a surgical technique which aims to restore hearing in people with deep hearing loss. However, outcomes of the surgery still exhibit a large variability between patients. Among the factors that contribute to variability the most important are morphological differences in anatomical structures between patients and incorrect implant placements. In order to address these issues, it would be desirable to have a functional model of the cochlea which incorporates inter-patients variability and simulate electrode placement. To this end, we present a finite element model which captures the interaction between the cochlear partition, modeled as an elastic solid with finite deformation, and the perilymph fluid, modeled as a compressible, viscous fluid. Numerical results show that the membrane responds to changes in the stimulation frequencies.