In a channel contained fuel bundle for a boiling water nuclear reactor, an improved channel is disclosed. The channel contains a plurality of fuel rods held in spaced apart relation by at least upper and lower tie-plates and/or spacers. In the reactor, the channel contains fuel rods extending between a lower support plate and an upper support grid. When the reactor is operating, the channel confines water flow intimately about the rod bundle on the inside and assures steam generation in a predictable pattern. Water exterior of the channel is at a different and typically lower pressure. To accommodate control blades (which control the fission process) outside of the fuel bundles, the channel is provided with a polygon cross section, most typically a square cross section. In operation, the flat walls tend to bulge due to primarily pressure effects but also due to thermal and radiation effects. An improved channel is disclosed utilizing a lesser volume of metal which includes corrugated sides providing reinforcement of the side walls against bulge. The corrugations can protrude toward either the inside or the outside of the channel. An embodiment including thick corner sections is disclosed. These thick corner sections provide fixed supports for thin sides and at the same time improved beam resistance to seismic loading.