A tonneau cover assembly is provided having a plurality of substantially rigid panels inserted between the fabric and the bows and then locked into place and/or supported by snap-fit elements connecting to the peripheral frame of the tonneau cover. The snap-fit elements can also serve to positively locate the bows with respect to the frame. The panels can be closely dimensioned with respect to the distance across the frame or spaced somewhat to accommodate insertion about frame hinges and/or close fitting fabric, bows and frames. Two sided adhesive tape can be used between the panels and the snap-fit elements and the bows to maintain panel placement in the event that the assembly is to be a permanent aspect of the tonneau cover. Panels can also be perforated for weight reduction and/or cost savings without significant loss of theft security. Panels can be padded for impact absorption without permanent deformation so as to maintain tonneau cover attractiveness despite significant wear and tear during use.