Pop-up cards are an interesting form of paper art with intriguing geometrical properties. It is labor-intensive and requires a high level of skill to generate two-dimensional objects that pop-up into realistic 3D objects. Howev-er, this special feature makes the design procedure of a pop-up card challeng-ing. This paper proposes a novel algorithm to create a v-fold pop-up card from a 3D model using a directed acyclic graph. The algorithm computes a class of elements containing planar pieces and connections that approximate an input 3D geometry. Moreover, the pop up card is foldable, stable, and intersection-free when open and closed. The proposed method is demonstrated with various paper pop-ups, and experimental examples are presented.