In this chapter, we consider the case where the initial stresses are of the same order as the elastic constants of the material of the beam. As was noted above, this is not a rare, but usual case in engineering. A typical case is thermal stresses in non-uniform structural elements. Note that the use of thermal stresses is widely used in the production of pre-stressed structural elements. Thermal stresses also play the role of initial stresses in continuous rails, see Chap. 2. Of course, the initial stresses are small as comparable with the elastic constants in the absolute value. We will make a transition from a three-dimensional problem of elasticity theory with initial stresses in a small-diameter body to a problem of beam theory.