A sound signal is transmitted to the cochlea through vibration of the middle ear that induces a pressure difference across the cochlea’s elastic basilar membrane. In an alternative pathway for transmission, the basilar membrane can also be deflected by vibration of the cochlear bone, without participation of the middle ear. This second pathway, termed bone conduction, is increasingly used in commercial applications, namely in bone-conduction headphones that deliver sound through vibration of the skull. The mechanism of this transmission, however, remains unclear. Here, we study a cochlear model in which the cochlear bone is deformable. We show that deformation of the cochlear bone, such as resulting from bone stimulation, elicits a wave on the basilar membrane and can hence explain bone conduction. Interestingly, stimulation of the basilar membrane can in turn elicit a wave of deformation of the cochlear bone. We show that this has implications for the propagation of otoacoustic emissions: these can emerge from the cochlea through waves of bone deformation.