The invention relates to an anaerobic digester (7) for producing biogas (25), comprising a tank (8) that can contain solid biomass (23) and having, in the upper part thereof, at least one region (9) for the admission of the solid biomass (23) and the evacuation of the residual digested solid biomass (19), over which a roof (10) can open and close, and at least one region (9') for the evacuation of the biogas (25). The invention also relates to a method for producing biogas and to an anaerobic digestion facility using a main digestion unit (1) particularly for supplying at least one anaerobic digester (7) containing solid biomass (23) with liquid digestate (5), and for receiving and storing the biogas produced by the at least one anaerobic digester (7).