Congestion is a major issue in the modeling of both animal aggregation and supply chains. Indeed, both systems face obvious physical limits : capacities of machine in supply chains [1] and non-overlapping constraints between individuals in social groups. As a paradigm of crowding and social group movement, we are interested in sheep herds. The behaviour of this gregarious animal is experimentally studied [5]. Let us focus on the displacement period of a sheep herd, where all animals move with the same speed. A macroscopic model for herds including speed and congestion constraints is derived from an individual based model. In order to enlight the congestion part in the dynamics, a singular limit of this macroscopic model is taken and leads to two phases in our herd : a congested and a non-congested one. We finally analyse the spatial transition between these two phases. Such a study of the congestion in self organized systems could be translated to supply chains context.