In this paper, we propose a method of estimating the contact force of a bone-conducted sound transducer with a two-degrees-of-freedom vibrating model. First, the electrical impedance of the transducer was measured by varying the contact force applied to 12 human subjects. The model was fit to the measurement electrical impedance by changing the damping coefficient. The results showed that the model's damping coefficient is related to the contact force. The fitting was valid when the contact force was below than 3.0 N. Second, a contact force estimation method utilizing the relationship between the damping coefficient and the contact force was proposed. The contact force was estimated by estimating the damping coefficient from the measured impedance and calculating the corresponding contact force from the damping-contact force curve. The estimation results showed that the proposed method achieves reasonable accuracy compared to a previous method using a neural network. Also, the proposed method can be achieved with only two calibration conditions, 0.3 N and 0.5 N, by employing a physical model. This drastically reduces the calibration process compared to the previous methods.