In this paper, we study a formation control scheme for a 1-D string of vehicles. Each member tracks the movement of its immediate predecessor but also the first vehicle tracks the position of the last member of the string. We discuss conditions for the stability of the full interconnected system and show that if a constant spacing policy is used, the stability of the system is lost after the string size exceeds a certain number depending on the model parameters (vehicles and controllers). Additionally, we study the use of a constant time headway spacing policy. If the associated time headway parameter is greater than a critical value, the interconnected system is stable and string stable for any string size. Finally, we show that if an independent leader vehicle is added to the formation and every follower has access to this leader position, the cyclic formation with a constant spacing policy can be made stable and string stable by appropriately selecting a design parameter.