A search for evidence of physics beyond the Standard Model in final states with multiple high-transverse-momentum jets is performed using 20.3 fb⁻¹ of proton-proton collision data at (Formula presented.) = 8 TeV recorded by the ATLAS detector at the LHC. No significant excess of events beyond Standard Model expectations is observed, and upper limits on the visible cross sections for non-Standard Model production of multi-jet final states are set. A wide variety of models for black hole and string ball production and decay are considered, and the upper limit on the cross section times acceptance is as low as 0.16 fb at the 95% confidence level. For these models, excluded regions are also given as function of the main model parameters.