Research antiplane problem for perfectly elastic body with reinforcing elements are made in a wide range of publications, their results and review can be found in [1-6], and others. However, the proposed solutions do not take into account the possibility of switching ligament in a single frame. By limiting the movement of the reinforcing inclusions bonding with each other, we get a higher rigidity and a different stress distribution pattern. Proposed in the report [7] scheme for solving the problem of the inclusions of a single frame, is used here for the analysis of elastic equilibrium space parallel absolutely rigid ribbons. To solve the problem using the apparatus of singular integral equations. Defined power surges on the inclusions, the stress intensity factors in the vicinity of their peaks, the relative displacement of points in space. The effect of the connectedness of inclusions on the stress-strain state of the composition.