NOVELTY - The substantially airtight shed for the aerobic biological treatment of putrescible organic matrixes, comprises hemispheric dome shaped structure having a circular-/a quadrilateral base with rounded off-/ straight angles, or box structure with four lateral rigid walls and a vaulted/sloping roof, a floor completely linked to the structure by airtight welding joints, and a floor integral with walls made of air-proof flexible material. The shed is maintained in an upright position by a reticular stress-structure or self-supporting structure because of an internal overpressure.    USE - Useful for the aerobic biological treatment of putrescible organic matrixes.    ADVANTAGE - The shed improves the treatment of putrescible organic matrixes without formation of stinking emissions, which affects healthy environmental nature and public health, and controls the growth of insects such as flies and mosquitoes. The shed is simple and economic.    DETAILED DESCRIPTION - The substantially airtight shed for the aerobic biological treatment of putrescible organic matrixes, comprises hemispheric dome shaped structure having a circular-/a quadrilateral base with rounded off-/ straight angles, or box structure with four lateral rigid walls and a vaulted/sloping roof, a floor completely linked to the structure by airtight welding joints, and a floor integral with walls made of air-proof flexible material. The shed is maintained in an upright position by a reticular stress-structure or self-supporting structure because of an internal overpressure. The walls and the floor are made of air-proof flexible materials, in which 20-90 % of the surface of the dome or the roof are made of transpirable membranes. The transpirable membranes are made of flexible fabrics, which are able to make air, water vapor and carbon dioxide and is impermeable to molecules. The size of the molecule is higher than the air, water vapor and carbon dioxide. The air-proof flexible material is impregnated with a thermoplastic or thermosetting resin that is able to guarantee the impermeability to the fabric. The length and the width of the shed are 2-40 meters and 12 meters. The height of the wall is 2-8 meter. The maximum height of the dome shaped structure is 2-10 meter and the base surface of the dome shaped structure is similar to the base surface of the box structure. The air-proof flexible material is anchored to the flooring or to rigid walls, and is sealed to assure air-tightness of the internal space. The transpirable membranes are of square, rectangular, circular and elliptic shape, with a surface of 200 m2 and are symmetrically arranged on the surface of the dome-shaped structure or on the roof of the box structure. The transpirable membranes are applied from the inside of the structure.    DESCRIPTION OF DRAWING(S) - The drawing shows a substantially airtight shed:    Air-proof material; (1)    Transpirant material. (3)