Fracture and deformation problems anticipated for the first wall of a future steady-state fusion power reactor are discussed. The stress sources considered are surface heat flux, irradiation-induced creep and swelling, and coolant pressure. Simple examples, such as a beam or a plate, as well as finite element analyses of more realistic structures from recent design studies, are used to explain the problems that are anticipated. Detailed two- and three-dimensional finite element analyses of a grooved first wall are presented to show that grooving the first wall is a potential solution for high thermal stress.