Three series of binary, FeTi (Ti-rich), FeAl and TiAl (Al-rich) alloy samples were produced in an argon arc furnace. An annealing treatment of 72 h at 1000 °C was applied to the samples, giving rise to different equilibrium microstructures depending on chemical composition. Their mechanical properties were studied through the determination of elastic constants that measure the stiffness of the elaborated materials. Young’s modulus of the binary alloys was determined using Resonance Ultrasonic Vibration (RUV). The accuracy of this technique was demonstrated. A scanning electron microscope (SEM) with an energy dispersive spectrometer (EDS) and X-ray diffraction (XRD) made it possible to identify intermetallic compounds FeTi and Fe2Ti, FeAl and FeAl2, and TiAl and TiAl2 in respective systems Fe–Ti, Fe–Al, and Ti–Al. The link between their composition, microstructure, and elastic properties was established.