It is widely acknowledged that the two major interoceanic canals of Suez and Panama play a central role in global shipping flows. However, this role has rarely been measured with precision both in terms of the geographic coverage and network topological properties of canal-dependent flows. Based on vessel movement data for containerships, this research clarifies the weight and share of canal-dependent flows globally and at the level of world regions, routes, and ports. It also estimates and maps the effects of removing canal-dependent flows from the network by means of graph-theoretical methods. While main results converge in showing a decreasing importance of canal shipping in the context of growing south-south trade exchanges, certain areas remain more dependent than others, such as Asia, Europe, and North America. The research also underlines factors of port vulnerability across the globe in relation with the two canals.