To predict the springback of double curvature plates is difficult. Springback has negative effects on forming efficiency and quality. A series of experiments were carried out to study the springback problem of Invar alloy smooth mould plate forming process based on the flexible square pressure head technique. The experiment aimed at punching different sail and saddle shaped plates. Due to the complexity of the forming mechanical state of the equipment, springback has certain uncertainties, but there are clear rules: The distance from the edge of the plate has an important impact on the springback, the springback of plate at middle position is obviously smaller than the edge; The larger the curvature is, the springback is smaller, but not stable; The springback of saddle shape is smaller than that of the sail shape. The results are useful to guide the forming of smooth sheet products with uniform deformation by flexible die.