For　the　first　time　the　cylindrical　coordinates　were　employed　to　study　the　heat　and　mass　transfer　in　the　steady　laminar　Casson　nanofluid　flow　over　a　stretching　cylinder　in　view　of　velocity　slip　and　convective　surface　boundary　conditions.　The　governing　partial　differential　equations　(PDEs)　were　transformed　into　highly　nonlinear　coupled　ordinary　differential　equations　(ODEs)　via　appropriate　similarity　transformations　and　then　solved　numerically　with　the　shooting　method.　The　effects　of　different　physical　parameters　on　velocity　profiles,　temperature　and　concentration　distributions　were　presented　graphically　and　analyzed　in　detail.　The　results　show　that　the　velocity　is　strongly　influenced　by　the　slip　parameter,　while　the　temperature　and　the　concentration　are　sensitive　to　the　Biot　number　and　the　Lewis　number　respectively.　An　increase　in　the　Casson　parameter　will　decelerate　the　flow　but　elevate　the　temperature　and　the　concentration.　Increasing　the　Brownian　motion　parameter　or　the　thermophoresis　parameter　will　raise　the　temperature.　A　larger　concentration　will　come　with　a　lower　Brownian　motion　parameter　or　a　higher　thermophoresis　parameter.　The　back　flow　exists　in　the　concentration　profile　for　relatively　large　values　of　the　thermophoresis　parameter.　©　2016　Editorial　Office　of　Applied　Mathematics　and　Mechanics.　All　rights　reserved.