Shortest path routing protocol intends to minimize the total delay between every pair of destination node and source node. However, it is also well-known that shortest path routing suffers from uneven distribution of traffic load, especially in dense wireless networks. Recently, several new routing protocols are proposed in order to balance traffic load among nodes in a network. One of them is Circular Sailing Routing (CSR) which maps nodes on the surface of a sphere and select routes based on surface distances. CSR has been demonstrated with better load balance than shortest path routing via simulations. However, it is still open that what load distribution CSR can achieve. Therefore, in this paper, we theoretically analyze the traffic load distribution of CSR in a dense circular wireless network. Using the techniques developed by Hyttiä and Virtamo, we are able to derive the traffic load of any point inside the network. We then conduct extensive simulations to verify our theoretical results with grid and random networks.