A sheathed building uses corrugated hat-channel furring channels to attach metal panels to an underlying wall structure in a semi-floating manner. The corrugated furring channels are attached to backsides of the metal panels using high-bond-strength tape, and the corrugated furring channels are “hooked” onto corrugated flanges of rail brackets that have been attached to the wall structure to secure the metal panels to the building. Using tape instead of conventional fasteners (e.g., screws or nails) reduces penetrations through the panels and reduces moisture behind the panels. The corrugations facilitate drainage of moisture from behind the panels and drying air circulation. In other embodiments such as a clapboard arrangement of metal panels, rail brackets are not used, and the corrugated furring channels are used to mount the panels in overlapping fashion with no fasteners penetrating through the panels.