Reversals in the ice/air surface slope are important in geomorphic and glaciological contexts, thus motivating consideration of the conditions under which they form. Surface slope reversals are seen in numerous places, such as ice rumples on ice shelves, as surficial lakes, and at the down-glacier end of Vostok lake, Antarctica. Such slope reversals can reduce or reverse the subglacial hydrological gradient, thereby rerouting subglacial water transport and possibly leading to the creation of subglacial lakes. Supraglacial lakes produced by slope reversals in ablation zones may aid in driving water-filled cracks that allow surface water access to the bed. Surface slope reversals, in the absence of a concomitant reversal in ice flow, indicate a local violation of the so-called ‘shallow-ice’ approximation, and in this circumstance the longitudinal deviatoric stress becomes critical in the stress equilibrium. Using a simple numerical model, we have explored the conditions under which surface slope reversals form for certain simple scenarios. The results indicate that ice which initially possesses a normal slope will tend toward a reversed slope if the ice is thinned, the bed is strengthened or the downstream buttressing is increased.