The elastic and magnetic properties, thermodynamical stability, deviation from stoichiometry and order/disorder transformations of phases that are relevant to Be alloys were investigated using density functional theory simulations coupled with phonon density of states calculations to capture temperature effects. A novel structure and composition were identified for the Be-Fe binary ε phase. In absence of Al, FeBe 5 is predicted to form at equilibrium above ∼1100 K, while the ε phase is stable only below ∼1500 K, and FeBe 2 is stable at all temperatures below melting. Small additions of Al are found to stabilise FeBe 5 over FeBe 2 and ε, while at high Al content, AlFeBe 4 is predicted to form. Deviations from stoichiometric compositions are also considered and found to be important in the case of FeBe 5 and ε. The propensity for disordered vs ordered structures is also important for AlFeBe 4 (which exhibits complete Al-Fe disordered at all temperatures) and FeBe 5 (which exhibits an order-disorder transition at ∼950 K).