To decrease vibration and noise in washing machines, lubricated friction dampers were installed. Although the structure of the friction damper is simple, it was not easy to develop a mathematical model for the dynamic behavior of the lubrication damper. To see the dynamic behavior of a friction damper, physical tests were carried out via a material testing machine by changing exciting amplitudes and frequencies. Complicated curves of spring characteristics and damping showed a hysteretic behavior. In this paper, a reasonable model for a friction damper is suggested. To model the hysteretic behavior of a friction damper, a Coulomb friction model was first applied. To get a refined model for stick and transition, an STV (stick transition velocity) model was analyzed. To develop a more accurate mathematical model, an MSTV (modified stick transition velocity) model was proposed. In the MSTV model, the friction force could be changed due to the velocity of the damper, and the damping force was calculated according to the relative velocity between the external displacement and the deformation of the sponge in the friction damper. The MSTV model was in a good agreement with the experimental results.