To reduce vibration and noise, various dampers have been applied to many devices such as vehicle suspensions and washing machines. In washing machines, lubricated friction dampers, usually of very simple structure, are installed. Despite the simple structure of these dampers, their dynamic behaviors do not lend themselves to easy mathematical model development, owing to nonlinear characteristics such as hysteresis, viscous elasticity, and other complications. To determine the characteristics of a lubricated friction damper, physical tests with various amplitudes and frequencies were carried out. The complicated lubricated friction damper curves obtained through the physical tests showed hysteretic behavior. In the present study, an analytical model of a hysteretic friction damper was developed, after which optimum parameter values and the maximum friction force were evaluated using an optimization technique. For description of the friction force as changed by the excitation amplitudes and frequencies, a relationship between the sponge velocity and the STV (stick transition velocity) was considered. To describe the hysteretic behavior of the friction damper, a Bouc-Wen model was adopted.