The production of K0S and Λ hadrons is studied in pp collision data at √s=0.9 and 7 TeV collected with the ATLAS detector at the LHC using a minimum-bias trigger. The observed distributions of transverse momentum, rapidity, and multiplicity are corrected to hadron level in a model-independent way within well-defined phase-space regions. The distribution of the production ratio of Λ to Λ baryons is also measured. The results are compared with various Monte Carlo simulation models. Although most of these models agree with data to within 15% in the K0S distributions, substantial disagreements are found in the Λ distributions of transverse momentum.