A　new　Bernoulli-Euler　beam　model　based　on　a　simplified　strain　gradient　elasticity　theory　is　established　in　the　current　investigation.　The　generalized　Euler-Lagrange　equations　and　corresponding　boundary　conditions　are　naturally　derived　from　the　Hamilton＇s　principle.　Then　axial　wave　propagation　of　small　scale　bars,　static　bending　of　cantilever　beams,　buckling　and　free　vibration　of　simply　supported　beams　are　analytically　solved　by　using　the　simplified　strain　gradient　beam　theory.　The　influences　of　the　Poisson＇s　effect　as　well　as　the　weak　non-local　strain　gradient　elastic　effect　are　discussed.　The　Poisson＇s　effect　is　found　to　increase　with　the　increase　of　the　beam　thickness　in　the　buckling　analysis,　while　the　higher-order　bending　moment　induced　by　stretch　strain　gradient　has　an　insignificant　influence　on　the　critical　buckling　load　in　our　numerical　analysis.　However,　the　effect　of　the　higher-order　bending　moment　is　very　significant　on　axial　wave　propagation　and　static　bending　of　micro-scale　beams.　The　current　work　is　very　helpful　in　understanding　the　microstructure-related　size　dependent　phenomenon.　(C)　2014　Elsevier　Ltd.　All　rights　reserved.