Abstract: A truck tonneau cover assembly (10) of the rollable storage type is disclosed as including a pair of elongated guides (22) and a cover (36) with slats (44) that move along converging front ends of the guides to provide the cover with an upwardly curved shape upon unrolling from a storage roll (34) so as to thereby be capable of shedding water. Enlarged side edges (38) of the cover (36) are received within grooves (24) of the guides with the cover extending through restricted guide slots (26) into these grooves to seal the cover edges and prevent the shed water from entering the truck bed (12) with which the cover assembly (10) is utilized. The guides (22) also have rear ends (30) that diverge such that the rear edge of the closed cover is straight and thus sealable with the vehicle truck tailgate (20). Antifriction bearings (48) mount the slats (44) on the guides (22) for forward and rearward movement along the truck bed.