This paper describes searches for the pair production of first or second generation scalar leptoquarks using 35  pb−1 of proton-proton collision data recorded by the ATLAS detector at s√=7  TeV. Leptoquarks are searched in events with two oppositely-charged muons or electrons and at least two jets, and in events with one muon or electron, missing transverse momentum and at least two jets. After event selection, the observed yields are consistent with the predicted backgrounds. Leptoquark production is excluded at the 95% CL for masses MLQ<376 (319) GeV and MLQ<422 (362) GeV for first and second generation scalar leptoquarks, respectively, when assuming the branching fraction of a leptoquark to a charged lepton is equal to 1.0 (0.5).