To provide a running apparatus with an even higher stability of straight traveling in the type which can control a direction by shifting the physical weight as in a snowboard and a skateboard and moreover, equipped with four wheels to allow running on bad roads.

Dampers 61a and 61b are arranged at a connection part of a shaft 4 to which front wheels are connected and a frame, and only when the shaft 4 turns upward, a damping force of the dampers resists the shaft but does not when the shaft is returned to the horizontal position thereof. As a result, sudden change as caused by the unevenness of the surface of the road can be provided in the angle between the shaft 4 and the frame while the shaft can be quickly returned to the horizontal position. By this constitution chattering due to the unevenness of the road can be prevented to ensure a stable running, and a sanse of steering is not weaken in the shifting of the physical weight.