New approaches to calculation of a profiled wall of the proposed beam of box cross section were formulated. A profiled wall of the beam was presented as an orthotropic plate and specifics of its work were taken into account. In calculations of a profiled wall, the actual deformed scheme was changed for the equivalent one. The accepted system at simplification works under load similarly to the original system and has similar characteristics. Power or parabolic displacement function depends on parameters of a corrugated wall (ordinates of a point on the height of the wall, the number of half-waves of stability loss). Solution to a fourth-order equation using the MatCAD computer complex was found. The result of solution to the differential equation is an original displacement function for a generalized model of the wall of a beam with a profiled wall of box cross section of trapezoidal outline. The displacements found allow obtaining values of stresses in the cross section of new structural forms of beams. The paper considers analytical dependence of the coefficient, obtained as a result of calculation, which represents the power of the argument of function of deformation of the middle beam’s axis on applied load. The function of square parabola was found to reliably correspond to a change in transverse deformations by height of the wall, which is proved by calculations using the method of finite elements. We present the possibility of using the resulting dependence for determining the stressed-strained state of the wall of a new structure of the beam with a profiled wall of the box cross section. The results, obtained by a mathematical algorithm of diagram of normal stresses, were graphically compared with traditional calculation. The feasibility of application of the presented methodological approach for beams with a profiled wall was proved because distribution of normal stresses by the traditional calculation method does not correspond to actual work of the wall. According to comparison of results of the conducted trial experiment with the presented method, the bending moment is accepted by flanges and sections of the wall, which are close to the flanges of the developed beams within (0.1÷0.2) hw