Abstract: Fe_73.5-xCo_xCu₁ Nb₃ Si_13.5B₉（x=0, 10 and 36.75） amorphous alloys were annealed with joule-heat treatment under the action of tensile stress（σ=30-350 MPa） for 10 s. The changes of stress-induced transverse anisotropy constant K, with σwere determined by the measurement of hysteresis loop. In order to study the stability of the magnetic hystersis loop, annealed samples of x=0 and x=10 were tempered at a constant annealing current for different tempering time. It is found that the proportional relation between K and σ is observed in three composition samples, which agrees to the tensile back-stress model proposed by Herzer. Additionally, K decreases rapidly in a short time and then decreases slowly with the increase of t. The change in short-time can be attributed to the relaxation of internal stress with time during annealing, and the long-time behavior can be explained by the flow unit model.