A cover assembly for a pick-up truck cargo box includes first and second rails attachable at the sides of the box. A cover has a first resilient hinge strip connecting a first panel to a second panel and allowing the first panel to pivot relative to the second panel. A third panel is attached to the second panel by a second resilient hinge strip, which allows the second panel to pivot relative to the third panel. The panels are supported on the rails. Latches on the panels hold the panels onto the rails. The cover may be opened by sequentially releasing the latches and folding the panels over onto each other.