This thesis describes searches for new particles predicted by the super symmetry (SUSY) theory, a theory extending beyond the current Standard Model of particle physics, using the ATLAS detector at the CERN Large Hadron Collider. The thesis focuses on searches for stop and sbottom squarks, the SUSY partners of the top and bottom quarks, which are expected to be lighter than the partners of the first and second generation quarks and therefore good candidates for the first evidence of SUSY. It describes novel techniques for estimating and rejecting the Standard-Model backgrounds to searches for these particles. It also includes an independent analysis seeking to constrain the Standard Model ttZ background process, which also represents the first ATLAS search for this rare process at the LHC. The stop squark analysis described, with substantial leading contributions from the author, is the first search for these particles at the LHC to use the jets plus missing transverse energy plus 0-lepton signature and provides the world's best limits on the stop mass for light neutralino LSPs. All in all, the thesis describes three different world-leading analyses in both Standard Model and SUSY physics and therefore represents a major contribution to the field.