Among the magnetostrictive alloys the one formed of iron and gallium (called "Galfenol" from its U.S. Office of Naval Research discoverers in the late 90's) is attractive for its low hysteresis, good tensile stress, good machinability and its rare-earth free composition. One of its applications is its association with a piezoelectric material to form a extrinsic multiferroic composite as an alternative to the rare room temperature intrinsic multiferroics such as BiFeO 3 . This study focuses on thin Fe 0.81 Ga 0.19 films of thickness 5, 10, 20 and 60 nm deposited by sputtering onto glass substrates. Magnetization reversal study reveals a well-defined symmetry with two principal directions independent of the thickness. The magnetic signature of this magnetic anisotropy decreases with increasing FeGa thickness due to an increase of the non-preferential polycrystalline arrangement, as revealed by transmission electron microscopy (TEM) observations. Thus when magnetic field is applied along these specific directions, magnetization reversal is mainly coherent for the thinnest sample as seen from the transverse magnetization cycles. Magnetostriction coefficient reaches 20 ppm for the 5 nm film and decreases for thicker samples, where polycrystalline part with non-preferential orientation prevails.PACS numbers: 68.55.-a, 68.35.bd,75.60.-d, 75.75.-c,75.80.+q, 81.15.Cd Keywords: Magnetization reversal, magnetic thin films. Thermoelasticity and electromagnetic elasticity (electroelasticity, magnetoelasticity). Beam, plate, and shell. Magnetic properties of monolayers and thin films. Magnetomechanical and magnetoelectric effect, magnetostriction. arXiv:1903.05397v2 [cond-mat.mtrl-sci]