The magnetic characteristics of Fe-based cast amorphous glass-coated microwires (with a positive magnetostriction constant) have been studied. The residual stress distributions in this type of microwires determine the domain structures and the switching field behavior. These wires are characterized by a rectangular hysteresis loop and can be used in measuring and identification engineering. A mathematical model that describes the process of the reversal magnetization of an amorphous microwire with the help of a large Barkhausen jump has been proposed. The model has been estimated with regard to the optimization of the signal-to-noise ratio. Using nonlinear model, the physical factors that cause the fluctuations of the start field have been studied. The results obtained do not contradict the existing physical concepts concerning a domain wall motion and are more general and realistic in comparison with the previous model.