Despite the extensive literature that has been devoted to analytical and experimental investigation of the fracture of plates made of laminated composite materials (LCM) with stress concentrators (SC: notches, through-cracklike defects), this problem demands further study, and no generally accepted approach to its solution has yet been found (see the surveys in [1-4], for example). In this article, we use singular integral equations (SIE) to solve two-dimensional problems of the theory of elasticity, and we employ the principles of linear fracture mechanics (LFM) to develop a general approach that makes it possible to estimate the stress-strain state and predict the strength of flat composite structural elements with notches and through cracks in a complex stress state. We will examine an elastic anisotropic plate of constant thickness h occupying a finite multiply-connected region D that is bounded by the contour L. The contour consists of closed curves LO, L1, . . . , L k (L 0 envelops all of the remaining contours) and curvilinear internal slits (cracks) Lk+ 1, Lk+ 2 . . . . . L n (Fig. 1). We will assume that the origin of the