Beams and columns have been used for thousands of years in human-made structures. Beams were used in supporting roof structures in these ancient temples, but unfortunately many of these beam-supported roofs did not survive the shaking induced by historical earthquakes. Galileo Galilei is often credited with the first published theory of the strength of beams in bending. This chapter considers some applications of beam models in mechanics and engineering. In 1877, Lord Rayleigh introduced the rotatory inertia term in beam vibrations. For a cantilever type of canopy or beam, reinforcing cable force can be used to stabilize the beam. In the area of railway engineering, rail track is commonly modeled as beams on an elastic foundation. For thin beams, a phenomenon called shear locking, leading to unrealistically stiff behavior, has been observed. Beam element with linear interpolation or shape functions appears to be more susceptible to such numerical problems.