We study a broad class of regular and quasi-regular plane elastic frameworks of orthogonal structure. Main attention is paid for constructing some approximate theories for a compound rod of regular truss structure with elementary rectangular cell having two non-interacting diagonal elements. Particular cases of such a structure, namely, compound rods of regular and quasi-regular structure, may be obtained by excluding some group of elements from the general structure. Using approximate structural theories, we may describe the process of deformation of compound rods by using comparatively simple discrete one-directional boundary value problems. The effectiveness of the models proposed is studied for some specific examples.