The essence of this mathematical model consist in construction of the basic stress-strain state which is based on the a new hypothesis of vertical element, and an additional stress-strain state of the regional flat deformation arising of close rigidly jammed edge. It gives the chance more exactly to estimate of the strength aircraft structures near to irregularities of type of connections of the low aspect ratio triangular Delta wings, empennage, and rocket stabilize. The method of asymptotic integration of differential equations of three-dimensional theory of elasticity is applied. By means of special oblique-angled system of the coordinate relationship for the two of fringe problems. The problems of additional, stress-strain state of the frige flat deformation variational method of Vlasov-Kantorovich. For example, calculation of a plate of constant thickness showed that a significant contribution to the overall stress state introduced transverse normal and shear stresses, which in the classical theory of plates and shells are neglected.