In the presence of the thin-walled structures, such as plates “undesirable” notches and cracks for repair and to increase structural strength in the form of plates are used for thin elastic plates. The scientific literature mainly presented the results of studies on the effect of overlap on the strength properties of plates with cracks. In [1-9] has studied the state of stress of the thin plate with a crack reinforced plate, completely covering the crack and adhered to the plate over its entire surface. A method of enhancing the plate with a crack through the pad attached to the plate just continuously along its border, or only at certain points, the subject of [6,10-15]. The plates with notches, backed along its borders ribs, studied in [16,17]. Plate with a circular cutout, underpinned by the edge of the elliptical ring-shaped plate, is considered . A detailed review of the literature and the main results of the above issues, as well as other methods for enhancing the plates with defects are in [9,16,19-22]. In this paper we study the stress state of thin elastic infinite plate with an elliptical cutout, which is superimposed fully covered by the confocal elliptical pad and firmly attached to the plate along its border. Plate at infinity stretched a predetermined voltage, and on the border of the recess are given external force, situated in the plane of the plate. Analytical methods are complex potentials Muskhelishvili, studied the stress concentration on the connecting line to the lining plate and at the boundary of the cut. In the case of the degeneracy of the elliptic cutout crack are stress intensity factors at the crack tip. The examples, charts, and stresses the stress intensity factors, study their dependence on geometry, elastic and power parameters of the problem, a comparison with the case of a single plate with an elliptical cut (or crack) in the absence of lining. The case of a plate with circular cut reinforced concentric circular plate attached to the plate along its border, or along a circle, studied in detail in [23,24].