This paper deals with minimum-weight beams built with the minimum volume of beam material that can sustain the subjected load. In order to build a minimum-weight beam, the geometry of the strongest beam is analyzed, for which the values of the maximum beam behaviors are minimized at the given volume of material. For the structural analysis of such a beam, the theorem of least work is employed, considering strain energies of both bending and shear. Further, deflection curves are obtained using the successive integration method. The strongest section ratios, as determined by both the maxi-mini stress and deflection, are obtained from the results of the structural analysis. The beam geometry of the minimum-weight beam, which is described by the taper type, side number, volume, and cross sectional depth, is determined from the given allowable stress and deflection. In numerical examples, three kinds of end constraint are considered: hinged-hinged, hinged-clamped, and clamped-clamped beams.