A search for the supersymmetric partners of the Standard Model bottom and top quarks is presented. The search uses 36.1 fb-1 of pp collision data at √s = 13 TeV collected by the ATLAS experiment at the Large Hadron Collider. Direct production of pairs of bottom and top squarks (¯b1 and ¯t1) is searched for in nal states with b-tagged jets and missing transverse momentum. Distinctive selections are de ned with either no charged leptons (electrons or muons) in the nal state, or one charged lepton. The zero-lepton selection targets models in which the ¯b1 is the lightest squark and decays via ¯b1→b¯X01, where ¯X01 is the lightest neutralino. The one-lepton nal state targets models where bottom or top squarks are produced and can decay into multiple channels, ¯b1→b¯X01 and ¯b1→ t¯X±1, or ¯t1 → t¯X01 and ¯t1 → b¯X±1 , where ¯X±1 is the lightest chargino and the mass difference m¯X±1 - m¯X01 is set to 1 GeV. No excess above the expected Standard Model background is observed. Exclusion limits at 95% con dence level on the mass of third-generation squarks are derived in various supersymmetry-inspired simpli ed models.