Body mass is a fundamental physical property of an individual and has enormous bearing upon ecology and physiology. Generating reliable estimates for body mass is therefore a necessary step in many palaeontological studies. Whilst early reconstructions of mass in extinct species relied upon isolated skeletal elements, volumetric techniques are increasingly applied to fossils when skeletal completeness allows. We apply a new ‘alpha shapes’ (α-shapes) algorithm to volumetric mass estimation in quadrupedal mammals.α-shapes are defined by: (i) the underlying skeletal structure to which they are fitted; and (ii) the valueα, determining the refinement of fit. For a given skeleton, a range ofα-shapes may be fitted around the individual, spanning from very coarse to very fine. We fitα-shapes to three-dimensional models of extant mammals and calculate volumes, which are regressed against mass to generate predictive equations. Our optimal model is characterized by a high correlation coefficient and mean square error (r²=0.975, m.s.e.=0.025). When applied to the woolly mammoth (Mammuthus primigenius) and giant ground sloth (Megatherium americanum), we reconstruct masses of 3635 and 3706 kg, respectively. We considerα-shapes an improvement upon previous techniques as resulting volumes are less sensitive to uncertainties in skeletal reconstructions, and do not require manual separation of body segments from skeletons.