The tension of the thin plate with a rectilinear crack is considered. It is known that in the neighborhood of the crack appear compressive stresses, which at a certain level of tension could lead to local buckling of the plate. Of interest is the concentration of maximum tensile stresses in plates after buckling.The purpose of the study is to clarify the issue of whether buckling promotes crack growth or leads to the stabilization of deformations. For the analysis of the stress state of the plate in the initial post-critical stage the approximate analytical solution is suggested. The post-buckling stretching the plate with central crack is analyzed by the finite element method using ANSYS code . The effect of the buckling under tension of a plate with a central crack on the level of the stress state is estimated. An analysis of the stress state in the vicinity of the tip of the central crack under uniaxial tension shows that with possible local stability loss near the crack an increase in tensile stresses in the vicinity of the crack tip is observed, and, as a result, load leading to destruction should be reduced.