Linearised　inverse　ultrasonic　scattering　methods　based　on　the　Born　and　Kirchhoff　approximations　are　utilised　for　flaw　reconstruction　in　an　elastic　material.　The　flaw　shape　can　be　reconstructed　through　the　FFT　of　the　scattering　amplitudes　in　K-space.　Theoretical　backscattered　waveforms　are　calculated　for　cubic　defects　of　different　sizes,　using　the　software　Ansys　9.0.　Inverse　scattering　methods　are　then　used　to　reconstruct　the　defect　shapes.　From　the　results　of　this　reconstruction,　it　can　be　said　that　the　linearised　inverse　scattering　methods　are　effective　means　of　shape　reconstruction　and,　for　our　application,　they　can　reconstruct　a　defect　that　has　a　minimal　characteristic　size　of　2　mm.