The problem of bending of a beam of variable cross section occurs very often in the engineering prsctice. For their calculation, a well as for the beams of constant cross section, the application of Bernoulli — Euler hypothesis is customary, the justification of which in case of beams of constant cross section is confirmed in different cases of loading in numerous works by St. Ve-nant, Michel and others. For beams of variable cross section, however the justification of the application of Bernoulli — Euler hypothesis has not been sufficiently examined. The task of this paper is to compare of the calculation of the tension of beams of variable cross section (Fig. 1) loaded by a equally distributed load q according to the elastic theory and with the application of Bernoulli — Euler hypothesis. If we accept that in the calculation, according to the elastic theory, the stress of the beam parts (ribs and the half of the flanges) is two dimensional, accordingly their Airy functions of tension are biharmonious. In the selection of the abovl functions all boundary conditions at free contours are satisfied. On connecting lines of the rib and at the flanges act forces of their mutual influences. When the coefficients of stress functions are represented by the coefficients force function, from conditions identily dilatations of rib and flanges on their connecting lines, an infinite system of linear equations is obtained, the solution of which determines the function of the force and the function of stress, and therby gives also the stress state of the beam. In the case of calculated example a satisfactory precision is attainable, coinciding with dilatation (Fig. 2). By comparision of this precis method with the approximate it is seen that the Bernoulli — Euler hypothesis gives a satisfactory precision and accordingly its application in the engineering practice is quite justified.