Fast coronal mass ejecta interact strongly with the ambient interplanetary plasma and magnetic field into which they propagate. A shock forms in front of an ejection and the slower moving ambient plasma ahead is accelerated and deflected from its path. In this paper we argue that such flow accelerations and deflections of the ambient plasma must produce a draping of the ambient interplanetary magnetic field about the ejected material similar to that which occurs in the magnetosheath surrounding the earth's magnetosphere. The draping pattern should depend upon the overall size and shape of the ejection, its speed relative to the ambient plasma ahead, the orientation of the ambient magnetic field, and the position where the shocked plasma is sampled. At some locations upstream from an ejection draping leads to an enhancement of the out-of-the-ecliptic field component (BZ) at the expense of the ecliptic components (BX, BY). Although turbulence and fluctuations in the ambient field may confuse the observational situation, we suggest that draping probably plays an important role in producing intervals of strong and prolonged negative BZ in the ecliptic plane at 1 AU and thus also may be an important factor in stimulating geomagnetic activity. ¿American Geophysical Union 1987