The ALICE measurement of K(S)(0) and Λ production at midrapidity in Pb-Pb collisions at √(s(NN))=2.76 TeV is presented. The transverse momentum (p(T)) spectra are shown for several collision centrality intervals and in the p(T) range from 0.4 GeV/c (0.6 GeV/c for Λ) to 12 GeV/c. The p(T) dependence of the Λ/K(S)(0) ratios exhibits maxima in the vicinity of 3 GeV/c, and the positions of the maxima shift towards higher p(T) with increasing collision centrality. The magnitude of these maxima increases by almost a factor of three between most peripheral and most central Pb-Pb collisions. This baryon excess at intermediate p(T) is not observed in pp interactions at √s=0.9 TeV and at √s=7 TeV. Qualitatively, the baryon enhancement in heavy-ion collisions is expected from radial flow. However, the measured p(T) spectra above 2 GeV/c progressively decouple from hydrodynamical-model calculations. For higher values of p(T), models that incorporate the influence of the medium on the fragmentation and hadronization processes describe qualitatively the p(T) dependence of the Λ/K(S)(0) ratio.