3D　printing,　also　referred　to　as　additive　manufacturing　(AM),　offers　the　construction　industry　new　opportunities　by　enabling　complex　structural　members　with　economical　cost.　Wire　and　arc　additive　manufacturing　(WAAM)　is　deemed　the　most　promising　and　appropriate　technology　for　metal　construction　owing　to　its　capacity　to　generate　large-scale　elements　with　less　time.　Fundamental　studies　on　the　structural　behaviour　of　WAAM　elements　are　still　lacking　to　facilitate　their　engineering　application,　especially　regarding　the　numerical　studies.　To　this　end,　a　numerical　investigation　on　the　local　buckling　of　WAAM　stainless　steel　square　hollow　section　(SHS)　stub　columns　under　axial　compression　has　been　carried　out　and　reported　herein.　The　existing　experimental　studies　conducted　on　WAAM　SHS　were　used　as　the　basis　for　validating　the　finite　element　(FE)　analysis.　FE　models　were　established　utilizing　the　as-built　anisotropic　material　properties　to　consider　the　impact　of　geometric　undulations　related　to　the　WAAM　process　and　then　verified　by　test　results.　Parametric　studies　were　conducted　utilizing　the　developed　FE　models　to　encompass　a　broad　range　of　cross-section　dimensions.　The　suitability　of　three　design　methods　in　Eurocode　3,　AISC　370　and　the　continuous　strength　method　(CSM)　for　WAAM　SHS　was　assessed　and　discussed　based　on　experimental　and　numerical　data.　The　study　demonstrates　that　the　CSM　provided　the　most　accurate　predictions　compared　with　the　design　provisions　in　Eurocode　3　and　AISC　370.　To　make　it　more　suitable　for　WAAM　SHS,　a　modified　design　method　based　on　EN　1993-1-4:2006　+　A2:2020　was　suggested.