The paper studies the horizontal and vertical vibrations of axles and bodies as well as the rotational vibrations of axles which occur in trucks with leaf-springs. The paper presents a mathematical analysis of the problem and offers improvements.Equations of motions are applied to a model of a two-axle, leaf-spring truck of average weight~that is, a highly representative truck. Conditions of both locked brakes and unlocked brakes are analyzed. Results demonstrate that special vibrational effects can arise whose cause is the frictional force relationship between the tires and the street. This can lead to strong rotational vibrations of the tire-axle system if the brakes are locked; such is the cause of discontinuous tire marks at intersections. "Brake-hop" can occur when shock-absorbers are arranged eccentrically; redistribution of these dampers can lessen the effects.