This　paper　studies　the　three　dimensional　buckling　and　post　buckling　process　of　compressive　long　elastic　beam　confined　by　cylindrical　lateral　constraint　without　friction.　Based　on　theoretical　analysis　and　numerical　simulations,　four　stages　are　identified　and　characterized　as　the　compressive　axial　displacement　increases　from　zero:　initial　two　dimensional　shape,　small　three　dimensional　shape,　three　dimensional　helix　shape　and　three　dimensional　alpha　shape.　Critical　axial　displacement　at　the　transition　points　between　four　deformation　shapes　are　studied,　and　the　effect　of　geometrical　parameters　such　as　beam　length　and　constraint　size　on　critical　displacement　are　examined.　Special　emphasis　is　paid　to　identify　the　transition　points　from　three　dimensional　helix　shape　to　three　dimensional　alpha　shape,　and　the　transition　can　be　divided　into　jump　regime　(sharp　transition)　and　no-jump　regime　(smooth　transition)　based　on　the　criterion　whether　number　of　helical　periods　is　larger　or　smaller　than　one.　At　the　same　time,　critical　number　of　helical　periods　in　three　dimensional　helix　shape　is　linearly　correlated　with　a　nondimensional　geometrical　parameter.　©　2018　Elsevier　Ltd