Graphene is being studied for its use in many potential future applications such as a component of computer chips or for its transport properties. Deformation of a graphene sheet under an applied load is investigated using both analytical and numerical means. The stability of a vertical graphene sheet when pressed against a solid substrate is studied and the load at which the sheet may become unstable is found. Then further analysis is done when we let the length of the graphene sheet go to infinity. In this case the substrate only affects the bottom position of the infinitely long sheet and thus a boundary layer problem is analyzed. This work can be used as a foundation for further understanding of the mechanical behavior of graphene.