An important question at present in particle physics is whether the recently discovered boson with a mass of about 125 GeV is the Standard Model Higgs boson. A Standard Model Higgs boson with a mass of 125 GeV will predominantly decay to b-quark pairs. This work presents the author's contribution to the search with the ATLAS detector for a Standard Model Higgs boson produced in association with a W or Z boson and decaying to b-quark pairs. In order to search for the decay modes ZH → vvb¯b, WH → lvb¯b and ZH → l¯lb¯b, where l is either an electron or muon, events with zero, one or two electrons or muons are considered in 20:3 fb¯1 of 8 TeV LHC data. A Standard Model Higgs boson is not observed decaying to b-quark pairs, although neither is this decay mode ruled out. A Standard Model Higgs boson with a mass of between 110 GeV and 115 GeV is excluded. For mH = 125 GeV the observed (expected) upper limit on the cross- section times the branching ratio is found to be 2.16 (1.07) times the Standard Model prediction. For a Standard Model Higgs boson with a mass of 125 GeV, the best fit signal strength is μ = 1:09 +0:43-0:42 (stat) +0:44-0:37 (syst) = 1:09 +0:61-0:56. The combined results are consistent with a Standard Model Higgs boson with a mass of 125 GeV. The author's own work is presented, including estimation of systematic uncertainties on WH → lvb¯b modelling, and future ATLAS data selection methods for WH → lvb¯b searches. Overviews of underlying theoretical matters and the experimental facilities used are given.