<p>Within the framework of an approach based on the equations of linearized mechanics of deformable bodies, the stress-strain state of a body containing two parallel Mode I cracks is investigated, taking into account the action of initial (residual) stresses directed along the cracks. The proposed method for solving the plane problem involves representing stresses and displacements using potential harmonic functions and applying Fourier integral transforms to them, which allows the given boundary value problem to be reduced first to a system of paired integral equations, and then to a system of inhomogeneous Fredholm integral equations of the second kind. From the analysis of the asymptotic distribution of stresses in the vicinity of crack tips, analytical expressions for the stress intensity factors are obtained, and it is shown that due to the mutual interaction of cracks, both stress intensity factors <i>K</i>₁ and <i>K</i>₁₁ take on non-zero values. For a nonlinear elastic material with the Treloar elastic potential (a neo-Hookean body), the dependence of the stress intensity factors on the initial stresses and on the crack spacing normalized by the crack length has been numerically analyzed. A resonant change in the values of the stress intensity factors was found when the initial compressive stresses reach certain critical values, which correspond, for the material under study, to a local loss of stability of the equilibrium state in the vicinity of the cracks.</p>