The　rapid　development　of　flexible　electronic　devices　has　created　an　increasing　demand　for　soft　materials　with　superior　heat　dissipation　properties.　However,　accurately　measuring　the　thermal　conductivity　of　flexible　materials,　particularly　under　dynamic　conditions　such　as　tensile　strain,　remains　a　significant　challenge.　In　this　study,　we　present　a　steady-state　thermal　conductivity　measurement　apparatus　designed　to　operate　under　tensile　loading　conditions.　We　detail　the　system＇s　design　operational　procedures,　data　correction　methods,　and　performance　benchmarks.　The　apparatus　was　validated　using　standard　reference　materials,　including　quartz,　stainless　steel,　and　copper,　producing　thermal　conductivity　values　of　1.57　±　0.04　W　m−1　K−1,　16.46　±　0.39　W　m−1　K−1,　and　384　±　19.62W　m−1　K−1　(95　%　confidence),　all　deviating　from　the　reference　values　by　less　than　8　%.　Additionally,　we　investigated　the　strain-dependent　thermal　conductivity　of　a　liquid　metal/Polydimethylsiloxane　composite.　The　results　demonstrate　the　effectiveness　and　reliability　of　our　method,　establishing　a　solid　foundation　for　the　thermal　conductivity　measurement　of　flexible　materials　in　electronic　applications.　©　2025　Elsevier　Ltd