Teams of Unmanned Aircraft Systems (UAS) have played a major role in operations like emergency response, search and rescue operations, border patrol and convoy support. The UAS teams can align themselves in different 3-D formations such as diamond, wedge, sphere and ellipsoid to meet different operations requirements and respond efficiently to a changing environment. Within the formation, each UAS must avoid collision with the others, smoothly replace any agents that cannot maintain their place in the formation, and accommodate any agents that join. This research aims at developing a mathematical model to describe the geometric configuration of the UAS members in 3-dimensions while avoiding collision with other team members. The members of the UAS team, located at random positions in the mission space are attracted into a bounded geometric configuration and move around the mission space as a single unit. The 3D geometric configuration consists of a region bounded by two geometric surfaces within which the members of the team are required to operate.