Abstract: A large flat metal plate is formed to have a three-dimensional shape of compound curvature by locally heating to an elevated temperature along predetermined lines and then quickly cooling, as by using a torch which carries a water spray nozzle. The heating extends completely through the thickness of the plate, and cooling causes significant shrinkage in the plane thereof in a direction perpendicular to the line of heating. Heating is carried out along lines in a geometric pattern and in a preselected sequence involving all quadrants of the plate so that it experiences a gradual transformation overall. The plate is normally supported upon an underlying cradle shaped to the desired compound curvature.