This chapter addresses the couplings of elastic elements where the role of friction is crucial. Structural friction attained special attention owing to experimental studies which proved the dissipative properties of it, fairly often higher than other sources of energy dissipation and vibration damping. Some descriptions are based on the assumption that friction appearing in fast couplings obeys the Coulomb laws. The analysis shows that the vibration period of a system with such couplings is different from periods corresponding to conservative vibration. This difference can have a small value when the rod has a considerable length or when pressure and friction forces developed in the clamps are big. Low pressure, small friction coefficients or short elastic elements entail easily discernable differences in the vibration periods. Furthermore, for the parameters of a fixed system the vibration period remains a function of the vibration amplitude. The period becomes shorter when the oscillation decays systematically.