A numerical analysis has been carried out with respect to the equilibrium configuration of the partial dislocations constituting both screw-type and edge-type twins moving at velocities close to the transverse sound velocity. It is shown that the degree of oblateness of the twin decreases as either the stacking-fault energy or the twin velocity is increased. The partials comprising the edge-type twin become vertically aligned at the Rayleigh wave velocity whereas for the screw-type twins this vertical alignment takes place at the transverse sound velocity. A detailed analysis of the stress field in the vicinity of the twin front shows that shear stresses are such as to favor spontaneous dislocation loop nucleation in a plane normal to the propagation direction of the twin. On the other hand, the normal components of stress in the vicinity of the leading edge of a moving twin are such as to hamper crack propagation. This crack impedance however, is lost as soon as the twin becomes blocked.