A rectilinear crack in a thin elastic plate is considered. At tension of the plate in the perpendicular crack direction in the vicinity of the crack appear compressive stresses, which at a certain level of tension lead to loss of stability of the plane form of equilibrium plates. The purpose of the study is to clarify the issue of whether buckling promotes crack growth or leads to the stabilization of deformations. The stress state of the plate in the initial postcritical stage is investigated. The approximate analytical solution is suggested. The finite element method is used to solve the problem of stretching a plate after loss of stability. The effect of the loss of a plane form of deformation under tension of a plate with a central crack on the level of the stress state in the vicinity of the crack tip 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.