Friction is one of the most important problems in engineering systems while vibration is the dynamic motion of objects and the forces associated with it. Modeling of friction-induced vibrations in mechanical and moving bodies requires an accurate description of friction. Unfortunately, there is no universally accepted friction model or theory to cover general friction; on the other hand, the resultant vibrations often exhibit various nonlinear, transient, and unsteady features. Small changes in interfacial parameters could have significant effect on the resultant vibrations and dynamic forces associated with those vibrations. In the present work a mathematical model of friction induced vibrations between a moving mass on a fixed horizontal plane has been proposed and the effect of the different operating conditions has been studied.