The following chapters of this book are devoted to the asymptotic analysis of beams—structural elements occupying small diameter domains. In this chapter, we consider beams of constant cross-section made of homogeneous material (hereinafter referred to as uniform beams)Beamuniform. Such kind beams are traditional and widely used structural elements. The generally accepted opinion is that Euler and Bernoulli were the first to formulate a complete theory of beams. Their predecessors in attempts to construct a theory of beams were Galilei and da Vinci. It is known that the Euler-Bernoulli beam theory does not take into account the transverse deformation of the beam as a result of the Poisson effect, thus, does not correspond to the physics reality. Nevertheless, the Euler-Bernoulli beam theory does give correct formulas for calculating the bending stiffness of the beam.