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 ( b ¯ 1 and t ¯ 1 ) is searched for in final states with b -tagged jets and missing transverse momentum. Distinctive selections are defined with either no charged leptons (electrons or muons) in the final state, or one charged lepton. The zero-lepton selection targets models in which the b ¯ 1 is the lightest squark and decays via b ¯ 1 → b χ ¯ 1 0 , where χ ¯ 1 0 is the lightest neutralino. The one-lepton final state targets models where bottom or top squarks are produced and can decay into multiple channels, b ¯ 1 → b χ ¯ 1 0 and b ¯ 1 → t χ ¯ 1 ± , or t ¯ 1 → t χ ¯ 1 0 and t ¯ 1 → b χ ¯ 1 ± , where χ ¯ 1 ± is the lightest chargino and the mass difference m χ ¯ 1 ± − m χ ¯ 1 0 is set to 1 GeV. No excess above the expected Standard Model background is observed. Exclusion limits at 95% confidence level on the mass of third-generation squarks are derived in various supersymmetry-inspired simplified models.