Thick-walled　structures　are　widely　used　in　kinds　of　high-end　equipment.　As　the　most　conventional　method　adopted　to　manufacture　large-scale　structures,　multi-pass　butt-welds　are　one　of　the　most　critical　areas　prone　to　defects.　In　this　paper,　we　focus　on　the　quantitative　detection　of　crack　depth　in　a　V-groove　weld　using　laser-generated　surface　acoustic　waves.　A　two-dimensional　finite-element　method　with　Q345　steel　is　adopted　to　reveal　the　complicated　propagation　characteristics　of　laser-generated　surface　acoustic　waves　with　surface　cracks.　The　displacement　fields　are　discussed　to　show　the　wave　transmission,　reflection,　and　mode-conversion　phenomena.　The　main　propagating　wave　modes—P,　R,　R＇,　R＇r,　and　R＇t　waved—are　distinguished　with　the　help　of　the　out-of-plane　displacement　under　different　crack　depths　in　the　time　domain.　It　is　found　that　R＇r　can　be　used　to　locate　the　cracks　and　R＇t　can　be　used　to　quantify　the　depth　of　the　cracks.　©　2023　Institute　of　Physics　Publishing.　All　rights　reserved.