IRIS (International Reactor Innovative and Secure) is a modular, integral light water cooled, low-to-medium power reactor, which addresses the requirements defined by the US DOE for Generation IV reactors. Its integrated layout features a pressure vessel containing all the main primary circuit components: the internals and the biological shield, here described together with the pressure vessel, plus the steam generators, the pressurizer, and the main coolant pumps described in companion papers. For this reason the pressure vessel is a crucial component of the plant, which deserves the most demanding design effort. The wide inner annulus around the core is exploited to insert steel plates, in order to improve the inner shielding capability up to the elimination of the external biological shielding and to simplify decommissioning activities by having all the irradiated components inside the vessel.