An apparatus is provided for digesting samples. The apparatus includes a vessel, a closure, and a fluid transporting system. The vessel has a digestion chamber therein that contains a sample holder, e.g., with a plurality of weights, the holder being accessible through a vessel opening. Typically, a vessel flange circumscribes the chamber at the chamber's opening, and the closure has a closure flange that may interface with the vessel flange to form a fluid-tight seal against a digestion pressure and temperature within the chamber. The fluid-transporting system may direct digestion fluid out of the digestion chamber through a submerged outlet port and back into the digestion chamber through an inlet port that traverses through the closure or the vessel flange. Such a fluid transporting system may be set up to allow the sample holder have a high volumetric capacity, e.g., at least 75% of the chamber.