Because of the presence of high cyclic thermal stress, coolant pressure-induced primary stress, and disruption-induced high cyclic primary stress, ratcheting (i.e., incremental accumulation of plastic strain) in the first wall poses a serious challenge to the designers of the U.S. International Thermonuclear Experimental Reactor (ITER). Existing design tools, such as the Bree diagram in the American Society of Mechanical Engineers Boiler and Pressure Vessels Code, are not directly applicable to the U.S. ITER because of important differences in geometry and loading modes. Available alternative models for ratcheting are discussed, and new Bree diagrams, which are more relevant for fusion reactor applications, are proposed.