Based　on　the　nonlocal　continuum　theory,　the　nonlinear　primary　resonance　of　nano　beam　with　the　axial　initial　load　is　investigated.　The　amplitude-frequency　response　for　the　primary　resonance　is　derived　with　the　multiple　scale　method　and　the　stability　is　analyzed.　The　nonlinear　primary　resonance　of　nano　beam　is　discussed　with　the　influences　of　small　scale　effect,　axial　initial　load,　mode　number,　Winkler　foundation　modulus　and　the　ratio　of　the　length　to　the　diameter.　From　the　results,　the　typical　hardening　nonlinearity　can　be　observed.　Moreover,　some　significant　and　interesting　nonlinear　phenomena　can　be　found　for　the　primary　resonance　of　nano　beam.　This　work　is　expected　to　be　useful　for　the　design　and　analysis　for　the　nonlinear　dynamic　behaviors　of　structures　at　nano　scales.　Crown　Copyright　(C)　2014　Published　by　Elsevier　Ltd.　All　rights　reserved.