A tarping system for removably covering the open top of a container resting on a platform of a truck frame, or directly on the truck frame, includes a cover support structure extending upwardly from the pivoted platform, a tarping frame displaceably secured to the cover support structure, a covering medium secured to the tarping frame and dimensioned to protectably cover the container open top, a power system extending between the cover support structure and the tarping frame for raising the tarping frame and thereby the covering medium above the container open top to permit the container to be removed from the truck frame.