Results of a study for the medical applications of micro- and nanowires are described. The magnetic characteristics of glass-coated Fe-based cast amorphous microwires (with a positive magnetostriction constant) are proposed. 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 model that describes the process of the reversal magnetization of an amorphous microwire with the help of a large Barkhausen jump is proposed. The model is estimated with regard to the optimization of the signal-to-noise ratio. The results obtained do not contradict the existing physical concepts concerning a domain wall motion and are more general and realistic than the previous models.