A search for Higgs-boson pair production in the bb¯bb¯ final state is carried out with 3.2 fb−1 of proton-proton collision data collected at s=13 TeV with the ATLAS detector. The data are consistent with the estimated background and are used to set upper limits on the production cross section of Higgs-boson pairs times branching ratio to bb¯bb¯ for both nonresonant and resonant production. In the case of resonant production of Kaluza-Klein gravitons within the Randall-Sundrum model, upper limits in the 24 to 91 fb range are obtained for masses between 600 and 3000 GeV, at the 95% confidence level. The production cross section times branching ratio for nonresonant Higgs-boson pairs is also constrained to be less than 1.22 pb, at the 95% confidence level.3 MoreReceived 16 June 2016DOI:https://doi.org/10.1103/PhysRevD.94.052002This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.© 2016 CERN, for the ATLAS CollaborationPhysics Subject Headings (PhySH)Research AreasExtensions of Higgs sectorParticle productionPhysical SystemsHiggs bosonsHypothetical scalarsParticles & Fields