The　contact　force　distribution　between　the　core　member　and　the　external　member　of　a　buckling-restrained　brace　(BRB)　is　closely　related　to　its　deformation　mode,　and　it　directly　affects　the　working　state　of　the　extended　core　and　external　restraining　member.　This　study　focuses　on　a　pinned　BRB　with　extended　core　as　a　research　object　and　investigates　the　stress　state　of　a　BRB.　Based　on　the　specified　core　deformation　modes　and　contact　force　distributions,　the　contact　force　and　the　bending　moment　distribution　in　the　external　member　are　deduced.　Lastly,　by　considering　the　mechanical　characteristics　of　the　external　member　and　extended　strengthened　core　region　(ESCR),　their　strength　design　criteria　are　established.　In　the　theoretical　derivation　of　the　design　method,　the　influence　of　some　parameters　is　considered,　including　the　initial　geometrical　imperfection　of　the　external　member,　the　gap　between　the　core　and　the　external　member,　the　rigidity　reduction　of　the　restrained　strengthened　core　region　(RSCR),　and　the　change　of　contact　position.　Finite　element　numerical　verification　of　the　corresponding　theoretical　derivation　is　discussed　in　detail　in　another　paper　as　Part　II　(Jiang　et　al.,　2015).