<p>The stress-strain state of a unidirectional fiber composite with a crack in the matrix adjacent to the fiber has been investigated. The composite is under tension along the fiber direction. It is proposed to utilize the asymptotic method developed by authors, the primary concept of which involves decomposing the stress-strain state of an orthotropic body into two components with distinct properties linked by boundary conditions. The obtained analytical solutions allow taking into account the structural heterogeneity of the material. The distribution of contact stresses valid everywhere except the area around singular points is determined. Together with the constructed singular solution, these presentations provide a uniform solution of the problem applicable throughout the domain.</p>