A flexible automobile bra securable to the exterior surface of an automobile is constructed of at least one panel which absorbs mechanical impact, provides mechanical stabilization to inhibit flapping under windy or high-speed conditions, faciltates water drainage, and limits temperature rise of covered portions of the vehicle. The bra comprises at least one panel having a first, non-abrasive layer; a second thermal radiation reflective layer which is also preferably a thermally conductive, radar reflective metal; a third layer of elastomeric reticulated foam, which can be a radar-absorbing type; and a fourth layer of water impervious material which is preferably water vapor permeable. In an alternative embodiment, the reflective second layer is eliminated.