The observed speeds of coronal mass ejections are often below the estimated Alfv¿n speed but above the sound speed for the background solar corona. This suggets that slow magnetohydrodynamic shocks may form as mass ejections sweep through the corona. We argue on the basis of the Rankine-Hugoniot relations and the propagation of small-amplitude slow mode waves that the shape of a slow shock front would be flattened (with respect to a sun-centered sphere) or perhaps even concave outward (from the sun) and thus present a very different appearance from the fast coronal shock waves that have been commonly modeled as wrapping around a mass ejection. The region behind a slow shock front standing just off the top of a coronal mass ejection would extend well out beyond the visible flanks of the ejection. The deflections of coronal structures that are commonly observed well outside of these flanks (and which are inconsistent with a fast shock wrapped around the mass ejection) are consistent with the presence of the slow shock, whether they lie in the enlarged postshock region or in a region still further beyond. Although the flattering of the tops of some mass ejections suggests our proposed slow shock configuration, a true test of its existence awaits formulation of quantitative models and detailed comparison with observations. ¿ American Geophysical Union 1987