Plates are structural elements given by a flat surface with a given thickness h. The flat surface is the middle surface of the plate; the upper and lower surfaces delimiting the plate are at distance h/2 from the middle surface. The thickness is small compared with the in-plane dimensions and can be either constant or variable. Thin plates are very stiff for in-plane loads, but they are quite flexible in bending. Many applications of plates, made of extremely different materials, can be found in engineering. For example, very thin circular plates are used in computer hard-disk drives; rectangular and trapezoidal plates can be found in the wing skin, horizontal tail surfaces, flaps and vertical fins of aircraft; cantilever rectangular plates are used as nano-resonators for drug detection; and flat rectangular panels are largely used in civil buildings.

If the middle surface describing the structural elements is folded, shells are obtained. Such structures are abundantly present in nature. In fact, because of the curvature of the middle surface, shells are very stiff for both in-plane and bending loads; therefore, they can span over large areas by using a minimum amount of material.

Shells are largely used in engineering; some shell structures are impressive and beautiful. In automotive engineering, the bodies of cars are shells; in biomechanics, arteries are shells conveying flow.