Many new physics models predict the existence of neutral, weakly interacting, long-lived particles that can decay within the detector volume, producing a distinctive experimental signature. A search is performed for a pair of such particles, using proton-proton collision data at √s = 8 TeV collected by the ATLAS detector in 2012, corresponding to a total integrated luminosity of 20.3 fb-1. Novel techniques are developed for the reconstruction of displaced decays to hadronic jets in the inner tracking detector and muon spectrometer. No significant deviation is found from the number of background events expected from Standard Model processes. The data are interpreted in terms of Hidden Valley scenarios with a Z' boson mediator. This dissertation presents the first results for a heavy Z' boson decaying to displaced hadronic jets.