The analysis of rod cross-ply bending and stability of rod systems in the presence of cracks is the aim of this paper. Using Maxwell's theorem about the reciprosity of displacements and the linear fracture mechanics methods for research of mechanical properties of rod systems in presence of cracks, there were obtained the main equation of the cross-ply bending, its common solution, the expression of relation between the rod deflection and the distributing cross-force and transcendental equation for determination of interior boundary of critical fotrce of rod with a crack.