Drape folds are an important type of oil trap in extensional basins like the N Sea (e.g., Forties Field). The sedimentary layers conform to the topography and structure of the underlying basement structures - therefore their shape can be more irregular than compressional folds (compressional basins), being related to fault trends in the basement.
They can form by differential compaction over basement highs, tilted fault blocks (Figure 1), carbonate shelf rims or isolated sand bodies in mud. The world’s largest oil field is Ghawar in Saudi Arabia - the oil occurs in Jurassic carbonates draped over and compacted around a north-south trending basement high.
An outcrop example is given in Figure 2. The shale layers drape over a faulted limestone (and underlying shale) block. There is a nice example of gouge in the underlying fault plane, together with wedges of calcite cement.
Reference
Selley, R. 1998. Elements of Petroleum Geology. Elsevier, 526 p. 2nd Ed.