1. The yield criteria recommended for polymers, in which the effect of hydrostatic pressure is formally reflected, are insufficiently reliable and can be used in engineering computations only for special cases of loading. 2. The strength criteria of polymer materials should be included as an independent parmeter of the third invariant of the stress deviator. To define the structure of the criterion more precisely, it is necessary to acquire in a rational manner experimental data on the mechanical properties of polymers in a complex stressed state. 3. A discontinuity in the convexity of the limiting surface, which is associated with structural changes in the material and with a change in the deformation mechanisms of the polymers at high levels of hydrostatic pressure, is observed experimentally.