We　theoretically　investigate　the　thermophoresis　of　nanocylinders　in　the　free　molecule　regime,　wherein　the　nonrigid-body　effect　is　taken　into　account.　The　analytical　formulas　of　the　thermophoretic　forces　on　cylinders　suspended　in　both　simple　gases　and　binary　gas　mixtures　are　derived　for　the　two　limiting　collision　models,　i.e.,　specular　and　diffuse　scatterings,　based　on　the　gas　kinetic　theory.　In　the　limit　of　the　rigid-body　collision,　the　expressions　can　be　reduced　to　the　theoretical　results　of　Garcia-Ybarra　and　Rosner　[AIChE　J.　35,　139　(1989)].　The　thermophoretic　velocities　of　the　nanocylinders　(including　carbon　nanotubes　and　long-chain　n-alkanes)　have　been　evaluated　and　it　is　found　that　the　influence　of　the　nonrigid-body　effect　on　thermophoresis　is　significant　for　the　case　of　small　cylinder　radius　and　low　temperatures.