In this article is described the construction of a thread model of a hyperboloid of one sheet (H) and its asymptotic cone (C). It ia simple to make, requiring only cardboard and thread, and can be made collapsible and of pocket size if desired. The model consists of two hinged pieces of cardboard (intersecting planes π and ) on which are drawn circles S_H, respectively in which the planes meet H, and the concentric circles S_C, respectively in which the planes meet C. A number of generators of the same system on H are now represented by threads joining S_H and , and the corresponding parallel generators of C are represented by threads joining S_C and . In order to ensure that these generators are well spaced, those of C are taken at equal eccentric angles apart in a principal elliptic section. The main theorem used in the design is that if l a generator of C, then the tangent plane to C at points of l meets H in two generators both of which are parallel to l