This script has been written to demonstrate a comparison between the first and the second order theories for the elastic isotropic beams deflection. As it is known, the second order theory enables to include directly the influence of the normal forces along the beam on its deflection function. From the mathematical point of view, the differential equation adequate to the deflection function is written on the deformed configuration of this beam, so that the normal forces can play significant role in the beam strength. This script consists of the three parts - the first one describes the classsical deflection determination procedure for the single bay structure clamped at both edges and loaded with the triangular force decreasing from the right to the left end. The extra loading is applied in the form of a concentrated bending moment at the right edge of the beam. The main aim of the second section is to present the procedure related to the second order theory with a compressive force, whereas the third section is devoted to the second order model with tension.