Frictional vibrations, such as stick-slip motion and automobile-brake squeal, which occur when two solid bodies are rubbed together, are analyzed mathematically and observed experimentally. The conditions studied are slow uniform motion and relatively rapid simple harmonic motion of brake lining over a cast-iron base. The equations of motion show and the observations confirm that frictional vibrations are caused primarily by an inverse variation of coefficient of friction with sliding velocity, but their form and occurrence are greatly dependent upon the dynamical constants of the mechanical system. With a constant coefficient of friction, the vibration initiated whenever sliding begins is rapidly damped out, not by the friction but by the “natural” damping of all mechanical systems. The coefficient of friction of most brake linings and other organic materials was essentially invariant with velocity, except that the static coefficient was usually greater than the sliding coefficient. Most such materials usually showed a small decrease in coefficient with increasing temperature. The persistent vibrations resulting from the excess static friction were reduced or eliminated by treating the rubbing surfaces with polar organic compounds which produced a rising friction characteristic.