The swarm control choosing an elastic body as a virtual structure can realize large-scale deformation of formation, and meet the requirements of collision avoidance naturally. Firstly, the swarm is embedded in a geometrically exact beam. By using interpolation of convective strain in Lie algebra, the virtual elastic potential energy of formation is shaped to realize the formation transformation quickly. Secondly, an algorithm of swarm flexible formation for target-capturing is established. It can accurately characterize both positions and attitudes of individuals in the swarm for engineering implementation. Meanwhile, it is independent of coordinate choice and suitable for describing large overall motion of the swarm. The distributed algorithm can be implemented in parallel with a high computational efficiency. Finally, the simulation results demonstrate that the algorithm is applicable and effective in the actual scene.