Represented　by　the　element　free　Galerkin　method,　the　meshless　methods　based　on　the　Galerkin　variational　procedure　have　made　great　progress　in　both　research　and　application.　Nevertheless,　their　shape　functions　free　of　the　Kronecker　delta　property　present　great　troubles　in　enforcing　the　essential　boundary　condition　and　the　material　continuity　condition.　The　procedures　based　on　the　relaxed　variational　formulations,　such　as　the　Lagrange　multiplier-based　methods　and　the　penalty　method,　strongly　depend　on　the　problem　in　study,　the　interpolation　scheme,　or　the　artificial　parameters.　Some　techniques　for　this　issue　developed　for　a　particular　method　are　hard　to　extend　to　other　meshless　methods.　Under　the　framework　of　partition　of　unity　and　strict　Galerkin　variational　formulation,　this　study,　taking　Poisson＇s　boundary　value　problem　for　instance,　proposes　a　unified　way　to　treat　exactly　both　the　material　interface　and　the　nonhomogeneous　essential　boundary　as　in　the　finite　element　analysis,　which　is　fit　for　any　partition　of　unity-based　meshless　methods.　The　solution　of　several　typical　examples　suggests　that　compared　with　the　Lagrange　multiplier　method　and　the　penalty　method,　the　proposed　method　can　be　always　used　safely　to　yield　satisfactory　results.　Copyright　(C)　2016　John　Wiley　&　Sons,　Ltd.