In the present paper under the local-structural damage of the composite materials, the local curving of the reinforcing layers or fibers in the structure of these composites is understood. As is well known, these local curving in the structure of the composite materials may be the consequence of technological process under the action of various factors described by Tarnopolsky & Rose(1). In a point of view of fracture mechanics of the structural elements fabricated from the multilayered composite materials the obtaining of the sufficient quantitative information on the influence of the above-mentioned local curving to the stress distributions is of considerable importance. We should note that it is very difficult or just impossible to investigate these problems for the structural elements fabricated from such materials in terms of a piecewise homogeneous body model. Nevertheless, these problems can be solved in the framework of the continuum theory of Akbarov & Guz(,2), which allows us to take into account with very high accuracy the existence of the above curving through the constitutive relations of the multilayered composites. Taking into account of the above-stated in the present paper we discuss the plate fabricated from the multilayered composite materials with locally curved structures and investigate the stress distribution in this plate with the use of three-dimensional equations of the theory of elasticity by employing the semi-analytical FEM.