The results of a search for pair production of supersymmetric partners of the Standard Model third-generation quarks are reported. This search uses 20.1 fb−1 of pp collisions at s√=8 TeV collected by the ATLAS experiment at the Large Hadron Collider. The lightest bottom and top squarks ( b˜1 and t˜1 respectively) are searched for in a final state with large missing transverse momentum and two jets identified as originating from b-quarks. No excess of events above the expected level of Standard Model background is found. The results are used to set upper limits on the visible cross section for processes beyond the Standard Model. Exclusion limits at the 95 % confidence level on the masses of the third-generation squarks are derived in phenomenological supersymmetric R-parity-conserving models in which either the bottom or the top squark is the lightest squark. The b˜1 is assumed to decay via b˜1→b∼0χ1 and the t˜1 via t˜1→b∼±χ1 , with undetectable products of the subsequent decay of the ∼±χ1 due to the small mass splitting between the ∼±χ1 and the ∼0χ1 .