We present the results of experimental and theoretical studies of the limit surface shape for a filled elastic polymer of heterogeneous structure. The construction of the strength criterion for the studied material is realized by a semiempirical method, analogous to the Mohr theory. The limit surface is approximated by two trihedral pyramids, narrowing to a point in the region of positive principal stresses and expanding in the direction of hydrostatic pressure increase. An attempt is made to study the strength experimentally under conditions of hydrostatic tension of specimens of special construction, the results of which indicate the validity of the assumptions adopted relating to the shape of the limit surface.