Three adaptive hypotheses have been forwarded to explain the distinctive Neanderthal face: 1) an improved ability to accommodate high anterior bite forces, 2) more effective conditioning of cold and/or dry air, and, 3) adaptation to facilitate greater ventilatory demands. We test these hypotheses using three-dimensional models of Neanderthals, modern humans, and a close outgroup (H. heidelbergensis), applying finite element analysis (FEA) and computational fluid dynamics (CFD). This is the most comprehensive application of either approach applied to date and the first to include both. FEA reveals few differences between H. heidelbergensis, modern humans and Neanderthals in their capacities to sustain high anterior tooth loadings. CFD shows that the nasal cavities of Neanderthals and especially modern humans condition air more efficiently than does that of H. heidelbergensis, suggesting that both evolved to better withstand cold and/or dry climates than less derived Homo. We further find that Neanderthals could move considerably more air through the nasal pathway than could H. heidelbergensis or modern humans, consistent with the propositions that, relative to our outgroup Homo, Neanderthal facial morphology evolved to reflect improved capacities to better condition cold, dry air, and, to move greater air volumes in response to higher energetic requirements.