The stability problems of thin plates with different defects such as holes, inclusions and cracks under tension are investigated. Loss of planar form of deformation occurs due to the formation of compressive stress zones near defects. By the study of deformation and stability of plates of nanometer thickness should be taken into account the effect of surface stresses acting on the faces of the plate. With the decrease of thickness the surface stresses they could significantly change the bending stiffness of the plate and correspondingly the critical load at which the planar shape of deformation is lost. In this work we study the following problems of stability of thin plates under tension: the plate with circular hole, the infinite plate with circular inclusion, the ring-shaped plate, which is expanded of external forces, the infinite plate with the system of parallel cracks. The analytical results are compared with results of finite element modeling.