Mechanical metamaterials such as ones based on origami and kirigami achieve bulk shape change through coordinated rearrangements of their parts. Typically, bar and hinge models are used to model this behavior, while in reality the underlying material is a continuum. For instance, origami is made by folding paper, while kirigami is made by cutting holes from a rubber sheet. Motivated by kirigami, we study the response of a truncated nonlinear elastic wedge in a double limit where the truncation length and scale of the applied forces tend to zero. We prove that the classical Flamant solution (stress ~ 1/r) gives the leading order response of the wedge. Since the linear elastic stress blows up at the tip of the wedge, the choice of nonlinearity plays a key role. We show that the Flamant solution is correct for models with at least quadratic growth at infinity; the case of quadratic growth is borderline, as we also discuss. This is joint work with Paul Plucinsky (USC) and Dominik Engl (KU Eichstätt-Ingolstadt).