In this paper, using the technique of fracture mechanics and defect mechanics, a completely analytical method is proposed for determining the compliance matrix, or elastic modulus and Poisson's ratio, for fibrous composite materials in the presence of ring cracks. In contrast to the approaches found in the literature, which have exact expressions as a basis, and end with a numerical solution method, in this work, from the very beginning, the assumption of a small size of the defect was introduced. This assumption, together with the application of the self-consistency method, resulted in simple analytical expressions for the desired characteristics of the material, convenient for practical applications.