A method cycle of a method for layerwise production of a tangible object (5) comprises the successive steps of: solidifying predetermined parts of a liquid so as to obtain a solid layer (14) having a predetermined shape; separating said solid layer from a construction shape (6); and moving, relative to one another, the separated solid layer and the construction shape to a predetermined position relative to one another. Solidifying is carried out such that the solid layer and the construction shape have nonmatching shapes in the sense that all surface portions of a solid layer side (70) that are or have been in contact with a liquid contacting side (11) of the construction shape can not simultaneously be brought in full contacting engagement with the liquid contacting side.