A polytunnel structure is described which comprises a plurality of rows of leg members, and a plurality of cover support members, each cover support member being supported at one end by a leg of one of the rows, and at its opposite end by a corresponding leg of an adjacent one of the rows, wherein at least one of the cover support members is of tubular form of non-circular cross-sectional shape having a major axis and a minor axis, wherein, in use, the minor axis extends generally parallel to a ground surface upon which the polytunnel structure is used, and the major axis extends perpendicularly to the minor axis.