The study of the Neanderthal thorax has attracted the attention of the scientific community for more than a century. It is agreed that Neanderthals have a more capacious thorax than modern humans, but whether this was caused by a medio-lateral or an antero-posterior expansion of the thorax is still debated, and is key to understanding breathing biomechanics and body shape in Neanderthals. The fragile nature of ribs, the metameric structure of the thorax and difficulties in quantifying thorax morphology all contribute to uncertainty regarding precise aspects of Neanderthal thoracic shape. The El Sidrón site has yielded costal remains from the upper to the lower thorax, as well as several proximal rib ends (frequently missing in the Neanderthal record), which help to shed light on Neanderthal thorax shape. We compared the El Sidrón costal elements with ribs from recent modern humans as well as with fossil modern humans and other Neanderthals through traditional morphometric methods and 3D geometric morphometrics, combined with missing data estimation and virtual reconstruction (at the 1st, 5th and 11th costal levels). Our results show that Neanderthals have larger rib heads and articular tubercles than their modern human counterparts. Neanderthal 1st ribs are smaller than in modern humans, whereas 5th and 11th ribs are considerably larger. When we articulated mean ribs (size and shape) with their corresponding vertebral elements, we observed that compared to modern humans the Neanderthal thorax is medio-laterally expanded at every level, especially at T5 and T11. Therefore, in the light of evidence from the El Sidrón costal remains, we hypothesize that the volumetric expansion of the Neanderthal thorax proposed by previous authors would mainly be produced by a medio-lateral expansion of the thorax.