Ultraviolet spectra of α Tau (K5 III) obtained by the Hubble Space Telescope (HST) show many emission lines affected by broad absorption from the strong wind of this red giant star. For the Mg II h and k lines there is also a narrow absorption feature in the midst of the wind absorption that has been interpreted as being from α Tau\u27s wind-interstellar medium (ISM) interaction region (i.e., its astrosphere ). We try to reproduce this absorption using hydrodynamic models of the α Tau astrosphere, which show that stellar wind material heated, compressed, and decelerated at the wind\u27s termination shock (TS) can produce significant absorption at about the right velocity. By experimenting with different model input parameters, we find that...