The solidification progresses of rapidly quenching from high-tempersture melts to form amorphous alloy ribbons were analysed. It was pointed out that different regions of the amorphous ribbon have different advancing ways of solidification in the process of solidifying, thus different local stress fields will exist in these regions. The internal stress fields and the stress-magnetic anisotropies in different regions of the amorphous ribbon were calculated theoretically. The calculated results and their inferences can interpret satisfactorily the observed structures of the magnetic domain in the amorphous ribbons and some phenomena in the experiments of the domain's observations.