The behaviour of a thin flat plate under a uniform stress in one direction is studied. The plate consists of a homogeneous, isotropic, elastic-plastic material obeying the Hencky stress-strain equations with the von Mises yield criterion. The conditions of plane stress are assumed to hold throughout the material. It is shown that θ, the angle of inclination of the slip plane with a direction perpendicular to the applied force, is less than θ 0 for tensile forces and greater than θ 0 for compressive forces, ( θ 0= cos −1 2 3 1 2 is the value of θ for an incompressible material). Finally it is proved that the slip plane is a surface of instability and hence a possible surface of shear fracture.