A mud flap is attachable to a selected group of through-holes of a vehicle running board. Plugs clamp to inclined surfaces of the through-holes, thereby firmly affixing a bracket portion of the integrally molded mud flap body to the running board. A flap portion of the mud flap body is connected to the bracket portion of the mud flap body only by a hinge portion. The hinge portion has a straight front surface, a straight rear surface and a thickness that is less than the overall thickness of the mud flap body. The flap portion has at least one wall portion that does not conform to any yz plane, stiffening the flap portion and inducing it to rotate around the hinge portion as a unit when a front-to-rear shear force impinges on the flap portion. A notch may be formed to interrupt an otherwise convexly curved rear flap portion surface so to receive a downwardly depending running board reinforcing member when the flap portion flexes out of its rest position.