A gluing technique is used to construct a rigorous closed linear theory of the deformation of a plane regular elastic cyclic truss-type bar system. The determining relations of this theory are formulated in terms of the nodal displacements, the total elongations of the bar elements, and the initial forces in those elements. All are generally speaking functions of two discrete arguments that can be used to number the elements of the elastic system (the nodes and the bars connecting them). These relations are represented by static, physical, and geometric equations, including a compatibility equation for the total deformations (elongations) of the bars and forming, in the aggregate, a simultaneous closed system of partial-difference equations. Alternative problem formulations in the nodal displacements and in the initial forces in the rod elements are given within the framework of the theory, which resembles, in its discrete aspect, the plane problem of elasticity theory in polar coordinates, and certain generalizations are indicated. When problems are stated in the forces, the number of static unknowns could be reduced significantly by introducing a function as a discrete analog of the stress function. Application of the theory is illustrated with examples of cyclic loading of a truss structure, for which exact analytic solutions are derived in closed form.