In every fibre composite, including that based on staple fibres of different length, force transmission from undamaged fibre to a neighboring separated or ruptured one is the area that requires further investigation. In the present paper a problem of force transmittion between undamaged and ruptured fibre is resolved with contact layer method for 2 situations: 1. When the fibre is damaged, but the matrix remains intact; 2. When the matrix is damaged as well as the fibre. The authors coin the term ‘intensity of adhesive interaction’ and elucidate the role of this intensity as well as the rigidity of the matrix in the ‘velocity’ of stress applied to the ruptured fibre. In other words, the influence of the absolute magnitude (modulus) of the intensity of adhesive interaction on so called ‘inefficient’ length of the destroyed fibre (term well known in research literature on composite materials). It is preferable that the inefficient length is as small as possible: this gives advantage in strength of both the fibre and the composite. The stress-strain state of adhesive models is determined by the method of contact layer, worked out by prof. R.Turusov. Rigidity of the contact layer, which is the ratio of its shear modulus to its thickness, is used by the authors as a characteristic of the ‘intensity of adhesive interaction’. It is shown that the influence of the intensity of adhesive interaction is determinative for force transmission from the intact fibre to the ruptured one. The higher the intensity of adhesive interaction, the more narrow is the stress concentration zone next to fibre breaking and the more narrow is the maximum of normal stress in the fibre, and the higher and more narrow is the maximum of shear stress at the boundary of matrix and fibre. The role of Young’s modulus (i.e. rigidity) of the matrix is far less considerable. Although it undertakes a good proportion of stress in some carbon-carbon composites where the rigidity of the matrix is comparable with the rigidity of the fibres. In this case its breakage can be dangerous no fewer than the breakage of the reinforcing fibre. Adhesive strength is just a criterion of adhesive failure and does not influence the efficiency of force transmission directly.