We demonstrate the importance of accounting for the complex magnetic ground state and finite temperature magnetic excitations in theoretical simulations of structural and elastic properties of transition metal alloys. Considering Fe72Cr16Ni12face centered cubic (fcc) alloy, we compare results of first-principles calculations carried out for ferromagnetic and non-magnetic states, as well as for the state with disordered local moments. We show that the latter gives much more accurate description of the elastic properties for paramagnetic alloys. We carry out a determination of the magnetic ground state for fcc Fe-Mn alloys, considering collinear, as well as non-collinear states, and show the sensitively of structural and elastic properties in this system to the detailed alignment between magnetic moments. We therefore conclude that it is essential to develop accurate models of the magnetic state for the predictive description of properties of transition metal alloys.