We have examined the structural and mechanical properties of Fe-Al alloys at various Al concentrations with or without a small amount of Mn. For each disordered Fe-Al alloy, we considered sundry disordered configurations to determine the equilibrium structure. It was found that the disordered Fe-Al alloy with high Al content (~25 at%) becomes less stable and more brittle than its ordered counterpart DO3 second phase. To predict the ductility of Fe-Al alloys, we estimated Pugh's constant defined by the ratio between bulk and shear moduli and apply the Pugh's criterion. We found that an addition of a small amount of Mn may stabilize disordered solid solutions over the DO3 second phase. Moreover, the Mn addition also improves its mechanical properties making the disordered Fe-Al alloy more ductile than DO3.