We study theoretically the deposition of few layer graphene sheets onto a grooved substrate incorporating adhesion between substrate and sheet. We develop a model to understand the equilibrium of the sheet allowing for partial conformation of sheet to substrate. This model gives physical insight into recent observations of snap-through from flat to conforming states and emphasizes the crucial role of substrate shape in determining the nature of this transition. Our analytical results are consistent with numerical simulations using a van der Waals-like interaction. Finally, we propose a substrate shape that should exhibit a continuous, rather than snap-through, transition. © 2012 American Institute of Physics.