When two bodies slide on each other the asperities are engaged and deformed which causes the dynamic friction. By superposing ‎ultrasonic oscillation to one of the bodies, the friction force is reduced . The experiments show that the friction force may be reduced by ‎about 60 percent depending on material properties and the kinetics of the two bodies. This phenomenon is widely used in metal forming ‎and metal cutting. This phenomenon may be used as a replacement of lubricants in such processes due to its higher efficiency and less ‎pollution effects . ‎ In this research an elastic-plastic model for the surface contact is given which is capable of predicting the friction force when ultrasonic ‎vibrations are superimposed to macroscopic motion . The result of this model is compared with that of the experimental values. The ‎differences between these values are shown to be less than 10 percent . The result of the model is also compared with that of the Dong ‎model. The comparison show that the present model ‎‏ ‏‎ has better accuracy of the Dong model .‎