The　complementary　energy　principle　associated　with　the　modified　couple　stress　theory　(MCST)　is　proposed　and　proved　for　analyzing　the　size　effects　of　Euler　micro-beams　considering　support　movements　and　negative　Poisson＇s　ratio.　The　analytical　solutions　with　the　size　effects　are　obtained　and　analyzed　for　the　support　reactions,　internal　forces,　curvatures,　rotations　and　deflections　separately　based　on　the　principle.　The　results　show　that　the　support　reactions　and　internal　forces　are　greatly　affected　by　the　size　effects　when　the　support　displacements　are　considered.　It　means　that　the　size　effects　exist　in　piezoresistive　pressure　sensors　that　are　sensitive　to　stresses.　Moreover,　the　direction　changes　to　the　opposite　for　the　total　moment　when　the　ratio　of　the　material　scale　parameter　l　to　the　height　of　the　micro-beam　h　(l/h)　goes　from　0　to　1.　The　deflections,　curvatures　and　rotations　have　nothing　to　do　with　the　size　effects,　respectively,　if　the　support　movements　are　only　considered.　Negative　Poisson＇s　ratio　materials　may　be　a　good　choice　to　verify　the　controversial　issue　of　whether　Poisson＇s　ratio　should　be　considered　in　the　MCST　beam　model　for　the　micro-scale　experiments.　The　main　reason　is　that　the　influence　of　negative　Poisson＇s　ratio　on　the　size　effects　is　larger　than　that　of　positive　Poisson＇s　ratio　in　the　theoretical　analysis.　The　analytical　solutions　agree　with　the　published　data　for　the　deflections　and　rotations　without　the　support　movements.