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, FeBe5 is predicted to form at equilibrium above ∼1100 K, while the ε phase is stable only below ∼1500 K, and FeBe2 is stable at all temperatures below melting. Small additions of Al are found to stabilise FeBe5 over FeBe2 and ε, while at high Al content, AlFeBe4 is predicted to form. Deviations from stoichiometric compositions are also considered and found to be important in the case of FeBe5 and ε. The propensity for disordered vs ordered structures is also important for AlFeBe4 (which exhibits complete Al–Fe disordered at all temperatures) and FeBe5 (which exhibits an order–disorder transition at ∼950 K).