The problem of the pure flexion of the beam made of non-linear elastic material is observed in the work. The link between the stresses and deformations is taken as a grade function, which contains up to the third degree of deformation inclusive. The accepted law of elasticity implies different limits of solidity of the material in cases of tension and compression of the material of the beam in different ways.
   Different cases of the stress-deformation link are observed, and the capacity of the beam is calculated.