Fe-Al is one of the best corrosion resistant alloys at high temperatures. The flip side of Al addition to Fe is the deterioration of the mechanical properties. This problem can be solved by adding a suitable amount of third alloying component. In the present work, we use ab initio calculations based on density functional theory to study the elastic properties of Fe1-x-yCrxAly alloys for Al and Cr contents up to 20 at.%. We assess the ductility as a function of chemistry by making use of the semi-empirical correlations between the elastic parameters and mechanical properties. In particular, we derive the bulk modulus to shear modulus ratio and the Cauchy pressure and monitor their trends in terms of chemical composition. The present findings are contrasted with the previously established oxidation resistance of Fe-Cr-Al alloys.