In the mammalian cochlea, the basilar membrane separates two fluid‐filled ducts and vibrates in response to acoustic stimulation. In vivo measurements of a viable basilar membrane show that the membrane is very sensitive to low‐level acoustic stimulation. A finite element model of the cochlea has been developed that explicitly couples the fluid, mechanical, and electrical domains of the cochlea. The proper function of the cochlea relies critically on structural acoustic coupling as well as electromechanical active control. The high sensitivity of the basilar membrane to low‐intensity sounds is explained by the presence of somatic motility in outer hair cells. The outer hair cells convert electrical energy to mechanical energy, amplifying basilar membrane motion. Recent experiments show that the tips of the outer hair cells, the hair bundle, can also produce an active force at acoustic frequencies. Active force production by the hair bundle is included in the model to predict the effects of hair bundle motility on the basilar membrane vibrations. Our model allows us to answer important questions about the interplay of the various active forces in the cochlea; questions that are difficult to address by experiments alone.