A folding tonneau cover including a first substantially rigid panel having a laterally-extending front edge at least partially defined by an elongate edge rail, and a second substantially rigid panel having a laterally-extending rear edge at least partially defined by an elongate edge rail, the first and second panels having opposed exterior and interior sides. The first and second panels substantially lie in a plane when the cover is unfolded, the first and second panel exterior sides generally facing in a direction away from a first side of the plane when the cover is unfolded, the first and second panel exterior sides adjacently superposed when the cover is folded. The cover includes a hinge assembly having substantially rigid first and second portions pivotally connected together along a first pivot axis located on the one side of the plane, the hinge first portion affixed to the first panel edge rail, the hinge second portion affixed to the second panel edge rail. A seal is affixed to at least one of the first and second panel edge rails. When the cover is unfolded the seal extends from one of the first panel front edge and the second panel rear edge toward the other and is entirely disposed on the same side of the first pivot axis as is the plane.