A crack in an elastic solid is considered as a thin smooth notch, or cutout, whose boundary displays substantial curvature in the neighborhood of the edges. In this paper the biaxial stressed state of a plane with such a defect, when the ratio of the loads applied at infinity is of order epsilon greater than 0 relative to the transverse dimension of the notch is considered. The first terms of the uniform asymptotic form in the parameter epsilon of the exact solution are sought; it is important that one of the limiting problems is provided by the problem of elasticity for a plane with a cut, to whose sides a load defined by the geometry of the notch is applied. The asymptotic properties of the stressed field are investigated in solving the fracture problem, the criterion proposed by Novozhilov is employed.