Abstract: An inflatable building construction, in particular suitable for use as a tunnel greenhouse comprising a film which is kept in an operative condition doming a predetermined useful space through an air pressure that has been increased relative to the environment, and which film has longitudinal edges anchored to the ground, wherein, for anchoring the longitudinal edges of the film, at least one flexible hose or tube is used which lies on and/or against a longitudinal edge provided in a trench in the bottom and which is filled with a fluid under excess pressure, which hose or tube clamps the film edges in the trench.