Sixtus-Tonks experiment for an amorphous Fe77.5Si7.5B15 wire made by quenching in rotating water has been performed under a tensile stress sigma. The data are analyzed using the formula V-w = S (H - H-0), where V-w is the axial wall velocity, H is the steady field, and S and H-0 are constants. To study the wall shape and damping mechanism, tubular- and planar-wall eddy-current models are proposed, and complete sets of formulas are given, including the wall shape, the pulse waveform, and the damping coefficient. A comparison between the experiments and the model prediction indicates that the propagating wall in such amorphous wires is not conical as usually suggested, but close to planar. The damping is dominated by eddy currents at small sigma, but with increasing sigma to 915 MPa spin relaxation plays an equally important role.