Phenomena related to dry friction appear in poorly lubricated or non-lubricated contact surfaces of bodies in relative motion. Based on the well-known solutions to the problem of free vibration damped by constant friction forces the following characteristics of such a motion can be set forth. These include there is a finite number of zero solutions, successive amplitudes create an arithmetic sequence, the vibration period remains constant and is equal to that of undamped vibration, the vibration center is shifted and the motion freezes after a finite number of oscillations. The identification of the model for a shock absorber should be done through an experiment. In the identification it is especially desirable to determine the dynamic characteristics and the relations of the force to the displacements. Measurements have to be carried out under impulse-type excitations. They enable one to determine these characteristics in the form of hysteresis loops.