Except for the addition of modern material remains, the archaeological record is a finite resource, which means that, at some point in the future, there will be nothing left to find. In this paper, we model trends in archaeological discovery based on the growth of the field and the probability of site discovery. We compare this model to seven diverse datasets of archaeological discovery trends: (1) all sites from the state of Wyoming, USA; (2) high-altitude archaeological sites from the state of Colorado, USA; (3) mostly complete Neandertal crania; (4) monumental sites of the Maya Classic period; (5) proboscidean kill/scavenge sites globally; (6) Upper Paleolithic sites from Europe; and (7) a compilation of shipwreck discoveries. We forecast discovery trends over the current century. We show that, for all datasets, rates of discovery are in decline, and some segments of the record are near depletion.