A correlation between the morphology and the magnetic domain structure (DS) of atomically disordered fee single crystals (A1 phase) of the FePd alloy upon annealing in the presence of a uniaxial tensile load has been investigated by the polarization-optical technique and the method of powder patterns. It is shown that several mechanisms of relaxation of elastic stresses that arise upon the A1-L10 phase transformation participate in the process of transformation of a disordered A1 phase to an ordered L10 phase. A correlation between the change in magnetic DS and the structural state of the crystals at different stages of ordering has been established.