Hitherto unobserved long-lived massive particles with electric and/or colour charge are predicted by a range of theories which extend the Standard Model. In this Letter a search is performed at the ATLAS experiment for slow-moving charged particles produced in proton-proton collisions at 7 TeV centre-of-mass energy at the LHC, using a data-set corresponding to an integrated luminosity of 34 pb(-1). No deviations from Standard Model expectations are found. This result is interpreted in a framework of supersymmetry models in which coloured sparticles can hadronise into long-lived bound hadronic states, termed R-hadrons, and 95% CL limits are set on the production cross-sections of squarks and gluinos. The influence of R-hadron interactions in matter was studied using a number of different models, and lower mass limits for stable sbottoms and stops are found to be 294 and 309 GeV respectively. The lower mass limit for a stable gluino lies in the range from 562 to 586 GeV depending on the model assumed. Each of these constraints is the most stringent to date. (C) 2011 CERN. Published by Elsevier B.V. All rights reserved.