This paper presents the building of lightweight tensile structures with quadrocopters. The construction elements (such as ropes, cables, and wires) in this kind of structure are subject to tension forces. This paper identifies the basic building elements (nodes, links) required for the construction of tensile structures, and translates them into meaningful trajectories for quadrocopters. The use of a library of building elements is suggested. Hybrid force-position control strategies based on admittance control are exploited. Prototypical tensile structures are built by quadrocopters to validate the proposed approach. An accompanying video shows the building process.