As an example of the application of density functional theory (DFT) to materials design, we describe our use of ab initio calculations based on DFT to develop a new structural material: Gum MetalTM, a novel, multifunctional titanium alloy with a low Young's modulus and high strength. We first carried out calculations on elastic constants in several Ti-X binary alloys to obtain the basic principles on which to determine the compositional limitations of an alloy with a low modulus. The elastic properties in the Ti-based binary alloys were successfully estimated by ab initio calculations, with the result implying absolute elastic softening at the valence electron number per atom, e/a, of 4.24. We also studied the effects of additional elements experimentally and, by comparison with electronic-structure calculations, found two more key parameters (approximately representing bond strength and electronegativity), critical for the design of practical elastic properties. We discuss dislocation-free plastic deformation of Gum Metal and its relation to the absolute elastic softening at an e/a value of 4.24, and finally we discuss the prospects for future applications of DFT in structural materials.