A roll-up tarp apparatus for attachment to an open top truck trailer having a truck box, having end caps at each end that partially cover the top opening. Preferred embodiments include a flexible tarp having at least one magnet, even more preferably a plurality of magnets along each end of the flexible tarp, that are configured to releasably secure the flexible tarp to the end cap when the flexible tarp is in the secured position. Preferably, the flexible tarp is wound around an elongated roll bar that is secured to at least one arm that connects the elongated roll bar to the truck box and selectively activates movement of the elongated roll bar to move the flexible tarp from an open position to a secured position. Various embodiments include biasing members to bias the arm(s).