The high sensitivity and wide bandwidth of mammalian hearing are thought to derive from an active process involving the somatic and hair-bundle motility of the thousands of outer hair cells uniquely found in mammalian cochleae. To better understand this, a biophysical three-dimensional cochlear fluid model was developed for gerbil, chinchilla, cat, and human, featuring an active "push-pull" cochlear amplifier mechanism based on the cytoarchitecture of the organ of Corti and using the time-averaged Lagrangian method. Cochlear responses are simulated and compared with in vivo physiological measurements for the basilar membrane (BM) velocity, V-BM, frequency tuning of the BM vibration, and Q(10) values representing the sharpness of the cochlear tuning curves. The V-BM simulation results for gerbil and chinchilla are consistent with in vivo cochlea measurements. Simulated mechanical tuning curves based on maintaining a constant V-BM value agree with neural-tuning threshold measurements better than those based on a constant displacement value, which implies that the inner hair cells are more sensitive to V-BM than to BM displacement. The Q(10) values of the V-BM tuning curve agree well with those of cochlear neurons across species, and appear to be related in part to the width of the basilar membrane.