A stress-strain state is studied of a plane regular elastic system formed by two orthogonal families of rods working only in tension/compression and thin walls working only in shear. Using the glueing method, the rigorous linear theory is developed for these systems. In the frames of the theory presented, the problems are formulated alternatively in terms of displacements and of forces and generalizations of these formulations are given for the cases of damage to some rods and wall cuts as well as for a discrete physical heterogeneity. The force formulation of the problems is illustrated by examples of systems with one and two rows of internal nodes. Exact analytical solutions are found for the examples. Some numerical results are presented for the first solution.