We have studied the effect of tension and external field on the magnetization process in amorphous positive magnetostrictive Fe‐Si‐B wires. The radial stress created during the in‐rotating water quenching technique of producing these wires causes a radial anisotropy. Using a simple phenomenological model which assumes a continuous distribution for the values of these radial stresses, we fit the observed values of the remanence as a function of the applied longitudinal stress and obtain information about the stress distribution. We also explain in a consistent manner the dependence of the magnetization process on the applied longitudinal stress. On doing so, a value of the saturation magnetostriction constant &lgr;s=28×10−6is obtained for a Fe77.5Si7.5B15amorphous wire. In the stress dependence of the nucleation field for the Barkhausen jump we observe a minimum. A quantitative explanation for this minimum is given.