A tonneau cover apparatus for removable attachment to a cargo box of a pickup truck including a support frame assembly and a cover assembly. The cover assembly includes a plurality of pivotally interconnected rigid panels that can be folded up and secured to the cargo box such that respective upper surfaces of at least two of the plurality of rigid panels reside in an upright folded orientation. The tonneau cover apparatus further includes a mechanism for securing the at least two of the plurality of rigid panels in the upright folded orientation. A method of removably securing the tonneau cover apparatus to the pickup truck is also described, as is an alternate embodiment of the tonneau cover apparatus, wherein the cover assembly includes first and second pivotally interconnected rigid panels and a pair of hinge support mechanisms that generally restrict the way the second rigid panel pivots.