A suspension is provided for mud flaps to be deployed behind wheels of a vehicle. The suspension allows for resilient translation of the mud flaps, such as should they get pinched against a curb and the wheels. A housing is adapted to be coupled to a bumper or other frame portion of the vehicle. The housing supports a spring therein. Cables are coupled to opposite ends of the spring and also to one of the mud flaps. When downward forces are exerted on one of the mud flaps, the cable associated allows the mud flap to translate downward slightly and cause the spring to be extended. When the loads subside, the spring causes the mud flap to return. In one embodiment a single suspension suspends two mud flaps over separate wheels. In a second embodiment, the suspension supports a single mud flap over a single wheel or wheel set.