To investigate cochlear responses to bone-conducted (BC) tones, a two-dimensional nonlinear cochlear model is proposed in this paper. The proposed model comprises macromechanical and micromechanical behaviors that can be described by the Laplace equation and Neely and Kims model, respectively. An outer hair cells model is also included as the source of cochlear nonlinearities. Cochlear responses to air-conducted (AC) tones can generally be simulated through stapes vibration. However, in this study, sound pressure was employed to affect the cochlear ducts outer wall for simulating cochlear responses to BC tones. Both frequency- and time-domain solutions can solve the proposed model. Through simulation, a forward traveling wave in the cochlea can be observed for both AC and BC tones in the frequency-domain solution. The time-domain solution indicates compressive nonlinearity for both AC and BC tones. However, the degree of compressive nonlinearity is the primary differentiating factor for AC and BC tones. For lower and higher input levels, the degree of compressive nonlinearity for BC tones is respectively higher and lower than that for AC tones. The obtained simulation results thus corroborate that compared to AC tones, BC tones generate a cochlear traveling wave response with marginally different compressive nonlinearity.