One-component materials with unidirectional fibrous structure are a new class of structural materials that are mechanically similar to biological ones. These contain channel cracks (CC) and weak interfaces in the structure, which are the result of production technologies. Effect of the CC size and the shear strength of contacts between fibers were investigated in the three-dimensional analysis of the elastic and inelastic shear extensions at the interface of the cracked fiber in the bundle of undamaged fibers under tension. The fiber stacking in the bundle is hexagonal. The fiber cross-sections are regular hexagons. It is found that the energy dissipation at the interface of the cracked fiber, the stress intensity factor and the crack opening displacement for the crack in the fiber and the length of the interface with the non-zero shear stresses are determined by the product of the contact cohesive shear strength and the contact width. At the optimal cohesive shear strength of the interfaces, the channel cracks shall not prejudice to the basic strength characteristics of the material.