This　article　investigates　the　elastic　compound　buckling　behavior　of　latticed　columns　with　three　lacing　systems　under　two　boundary　conditions.　Valid　numerical　method　named　SEM,　that　conducts　buckling　analysis　using　strain　energy　of　bars　and　potential　energy　of　chords,　was　built　to　address　flexural,　torsional,　and　flexural-torsional　buckling　loads　along　with　their　overall　and　local　buckling　deformations.　Eurocode　3　and　finite　element　software　ABAQUS　were　used　to　validate　the　auxiliary　of　SEM.　Through　the　research　on　X-lacing,　E-lacing,　and　K-lacing　latticed　columns　under　two　boundary　conditions,　the　rigidity　of　bars　was　found　to　exceed　a　threshold　value　affecting　the　linear　buckling　load.　When　the　cross-sectional　area　of　lacing　bars　tends　to　0　or　threshold　value,　Eurocode　3　guidelines　were　imprecise　in　forecasting　the　linear　buckling　load.　Eccentricity　and　geometric　imperfections　would　decrease　the　buckling　capacity　of　built-up　columns　substantially.　The　K-lacing　columns　respond　more　sensitively　on　local　imperfections　than　the　X-lacing　and　E-lacing　columns　under　simply　supported　condition.　However,　for　the　columns　under　cantilever　state,　local　imperfections　have　no　significant　impact　for　the　three　lacing　columns.　In　addition,　the　numerical　results　of　nonlinear　buckling　load　and　equilibrium　path　from　SEM　considering　geometric　imperfections　are　close　to　the　output　of　finite　element　method,　validating　the　accuracy　of　SEM.