Abstract: A pneumatic structure in the form of a barrel roof which has openings at the opposite ends thereof includes outer and inner walls of a sheet or membrane material connected by a plurality of partition walls in the form of ribs provided therebetween to define a plurality of air compartments in the form of ribs between the outer and inner walls. The partition walls includes a plurality of openings for fluid communication between adjacent air compartments. The pneumatic structure has specific dimensions defined as follows. 1.20≦b/a≦1.35 1.10≦d/c≦1.35 0.2≦a/c≦0.5 where a: the maximum opening width of the pneumatic structure; b: the total width of the pneumatic structure; c: the effective height (between ground and the maximum height of the inner wall; and d: the total height (between ground and the maximum height of the outer wall.