A method for layerwise production of a tangible object, the method comprising: - providing a construction shape, wherein the construction shape is a flexible foil; and - repeatedly performing method cycles, each method cycle comprising the steps of: - providing a liquid layer on a liquid contacting side of the construction shape of limited height that does not contact the tangible object; - moving, relative to one another, using a moving means, the construction shape to a predetermined position relative to the tangible object, for carrying out a successive such method cycle for solidifying a predetermined area of a successive such liquid layer; - solidifying, using solidifying means, a predetermined area of a layer of the liquid; - removing unsolidified parts from the tangible object so as to obtain a solid layer of the tangible object, the solid layer thus having a predermined shape; wherein for at least one of said method cycles, upper or lower parts of the moving means are brought in pressing contact with a side of the construction shape opposite to the liquid contacting side, the pressing contact being realized by a sliding or rolling movement of the moving means along said construction shape, and wherein: - the moving means are moved along the tangible object; and - the solidifying means are moved along the tangible object; such as to move the construction shape to bring the liquid layer in contact with the tangible object while the solidifying means are being operated, for carrying out said moving of said construction shape and said solidifying of said predetermined area to take place simultaneously. - providing a construction shape, wherein the construction shape is a flexible foil; and - repeatedly performing method cycles, each method cycle comprising the steps of: - providing a liquid layer on a liquid contacting side of the construction shape of limited height that does not contact the tangible object; - moving, relative to one another, using a moving means, the construction shape to a predetermined position relative to the tangible object, for carrying out a successive such method cycle for solidifying a predetermined area of a successive such liquid layer; - solidifying, using solidifying means, a predetermined area of a layer of the liquid; - removing unsolidified parts from the tangible object so as to obtain a solid layer of the tangible object, the solid layer thus having a predermined shape; wherein for at least one of said method cycles, upper or lower parts of the moving means are brought in pressing contact with a side of the construction shape opposite to the liquid contacting side, the pressing contact being realized by a sliding or rolling movement of the moving means along said construction shape, and wherein: - the moving means are moved along the tangible object; and - the solidifying means are moved along the tangible object; such as to move the construction shape to bring the liquid layer in contact with the tangible object while the solidifying means are being operated, for carrying out said moving of said construction shape and said solidifying of said predetermined area to take place simultaneously. - providing a liquid layer on a liquid contacting side of the construction shape of limited height that does not contact the tangible object; - moving, relative to one another, using a moving means, the construction shape to a predetermined position relative to the tangible object, for carrying out a successive such method cycle for solidifying a predetermined area of a successive such liquid layer; - solidifying, using solidifying means, a predetermined area of a layer of the liquid; - removing unsolidified parts from the tangible object so as to obtain a solid layer of the tangible object, the solid layer thus having a predermined shape; - the moving means are moved along the tangible object; and - the solidifying means are moved along the tangible object;