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 root s = 13 TeV collected by the ATLAS experiment at the Large Hadron Collider. Direct production of pairs of bottom and top squarks ((b) over bar (1) and (t) over bar (1)) is searched for in final states with b-tagged jets and missing transverse momentum. Distinctive selections are de fi ned with either no charged leptons (electrons or muons) in the fi nal state, or one charged lepton. The zero-lepton selection targets models in which the (b) over bar (1) is the lightest squark and decays via (b) over bar (1) -> b((chi) over bar1)(0), where (chi) over bar (0)(1) is the lightest neutralino. The one-lepton fi nal state targets models where bottom or top squarks are produced and can decay into multiple channels, (b) over bar (1) -> b((chi) over bar1)(0) and (b) over bar (1) -> b((chi) over bar1)(+/-), or (t) over bar (1) -> t((chi) over bar1)(0) and (t) over bar (1) -> b((chi) over bar1)(+/-), where (X) over bar (+/-)(1) is the lightest chargino and the mass difference m((chi) over bar1)(+/-) - m((chi) over bar1)(0) is set to 1 GeV. No excess above the expected Standard Model background is observed. Exclusion limits at 95% con fi dence level on the mass of third-generation squarks are derived in various supersymmetry-inspired simpli fi ed models.