The present paper considers variable bending of a three-layer elastoplastic bar with a compressible filler in the neutron flux. To describe kinematic properties of an asymmetric through thickness pack we have accepted the hypotheses of a broken line as follows: Bernoulli’s hypothesis is true in the thin bearing layers; Timoshenko’s hypothesis is true in the compressible through thickness filler with a linear approximation of displacements through the layer thickness. The filler’s work is taken into account in the tangential direction.