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. The  physical stress-strain relations correspond to the theory of small elastoplastic deformations. By the variational method a system of differential equilibrium equations has been derived. The kinematic conditions of simply supported faces of the bar on the immovable in space rigid bases are presumed on the boundary. The solution of the boundary problem is reduced to the search for four functions, namely: deflections and longitudinal displacements of the medial surfaces of the bearing layers. An analytical solution has been derived by the method of elastic solutions by using the Moskvitin’s theorem about variable loadings. Its numerical analysis has been performed for the case of the uniform distribution of the continuous and local loads.