In　this　paper,　a　new　multi-vehicle　formation　control　method　based　on　second　order　terminal　sliding　mode　control　(SOTSMC)　is　proposed.　The　bounded　disturbances　and　uncertainties　from　modelling　and　external　factors　such　as　gusts　and　vortices　are　considered.　The　conventional　sliding　mode　formation　controllers　are　also　investigated　and　designed.　To　improve　the　performance　of　integral　sliding　mode　controller　(ISMC),　especially　chattering　phenomenon　and　finite-time　stability,　a　second　order　non-singular　terminal　sliding　mode　surface　based　on　an　integral　sliding　surface　is　introduced　to　ensure　that　the　nonlinear　formation　system　converges　to　sliding　mode　surface　from　arbitrary　initial　states　in　finite　time.　The　Lyapunov　stability　is　proved　and　total　converge　time　is　calculated.　Finally,　to　verify　the　performance　of　the　proposed　SOTSMC　formation　controller,　a　comparison　between　the　ISMC　and　the　proposed　method　is　conducted　in　the　simulations　with　a　formation　consisting　of　two　followers　and　one　leader　which　tracks　two　different　prescribed　paths.　©　2019,　ICIC　International.　All　rights　reserved.