Magnetic properties related to anisotropy and stress are measured on long strips and toroids of three metallic glasses based on iron and nickel. The anisotropy scales as the magnetostriction. This suggests that magnetostrictive anisotropy is strong in these materials and that their average internal stress is comparable, being on the order of 108 dyne/cm2. The initial stress sensitivity of the remanent magnetization is large and is well predicted by simple theory. Barkhausen structure observed upon magnetization reversal suggests a magnetostrictive interaction between domain walls and pinning centers. Stress‐relieved toroids of these metallic glasses of finite magnetostriction show core loss decreasing with magnetostriction and approaching that of carefully annealed permalloys (λs?0) at 1000 gauss and 104 Hz.