We present results of theoretical and computer study of linear chain-like and complicated labyrinth structures in magnetic gels and suspensions as well as effect of these internal structures on macroscopic elastic properties of the composites. Our results show that at a certain threshold deformation, the structures experience a rupture which provokes a fall down of the macroscopic elastic stress, induced by the deformation. This effect is detected for both shear and tensile deformations. The results of calculations are compared with experimental data's.