The paper presents theoretical foundations of a crack arrest technique applied to composite plates. The approach is based on reinforcement of the original structure with thin tough layers. These layers reduce the stress field around the crack tip resulting in its effective arrest. The theory utilizes the existing solution for a crack in an anisotropic sheet. It is shown that the addition of tough layers results in a decrease of displacements and stresses by a single factor. This factor is evaluated using the principle of virtual work. All crack tip stresses and displacements, as well as the components of the strain energy, are expressed in terms of real functions. To the best knowledge of the authors, this is the first such presentation of these parameters for a general case of an arbitrary directed crack in arbitrary laminated layers.