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.