Stick-slip sliding is observed at various scales in fault sliding and the accompanied seismic events. It is conventionally assumed that the mechanism of stick-slip over geo-materials lies in the rate dependence of friction. However, the movement resembling the stick-slip could be associated with elastic oscillations of the rock around the fault, which occurs irrespective of the rate properties of the friction. In order to investigate this mechanism, two simple models are considered in this paper: a mass-spring model of self-maintaining oscillations and a one-dimensional (1-D) model of wave propagation through an infinite elastic rod. The rod slides with friction over a stiff base. The sliding is resisted by elastic shear springs. The results show that the frictional sliding in the mass-spring model generates oscillations that resemble the stick-slip motion. Furthermore, it was observed that the stick-slip-like motion occurs even when the frictional coefficient is constant. The 1-D wave propagation model predicts that despite the presence of shear springs the frictional sliding waves move with the P wave velocity, denoting the wave as intersonic. It was also observed that the amplitude of sliding is decreased with time. This effect might provide an explanation to the observed intersonic rupture propagation over faults.