Results on the FMR investigation of the effect of applied tensile stresses on the surface magnetic anisotropy of Co6
_{8.25}
Fe
_{4.5}
Si
_{12.25}
B
_{15}
amorphous glass-covered wires are reported. Axially applied stresses lead to a decrease of the resonance field and absorption intensity that correspond to the main resonance peak, indicating a reinforcement of the circumferential magnetoelastic anisotropy from the wire's surface region. The FMR spectra determined at 8.5 GHz -- the lowest employed frequency of the microwave field -- display a compound aspect, i.e. a secondary resonance peak is observed at slightly larger values of the dc magnetic field. This fact indicates that one can detect a region with different anisotropy direction towards the wire's inner zone when the magnetic penetration depth is large enough. The obtained results are valuable as regards the sensor applications of such materials.