On the stress-strain curve obtained in simple tension experiments, there is a region of instability due to the neck formation. In the theory of plasticity, conditions for the transition to an unstable state and appearance of the maximum point on the stress-strain diagram are determined. These condition were derived under the assumption of the material incompressibility. However, this assumption cannot be justified, since in the neck region, there are numerous damages (pores, micro-cracks), i.e., the material is compressible. With the current coefficient of lateral deformation, the authors formulate a condition for transition to an unstable state in a compressible plastic medium.