In　situ　electron　backscattering　diffraction　(EBSD)　investigations　were　conducted　on　polycrystalline　NiTi　tube　specimens　during　tensile　and　compressive　deformation.　The　long-range　cooperative　and　catalytic　martensitic　transformation　under　tension　induces　the　transformation　to　proceed　in　the　form　of　helical　Luders　band.　Propagation　of　the　band　is　closely　related　to　the　spatial　distribution　of　the　orientations　of　individual　grains.　In　uniaxial　compression,　the　larger　variation　in　Schmid　factors,　and　consequently　the　larger　variation　in　the　critical　transformation　stresses　among　grains,　leads　to　a　homogeneous　martensitic　transformation,　and　therefore　the　absence　of　the　Luders　band.　To　interpret　the　observed　tension　compression　asymmetry,　a　crystallographic　model　of　the　critical　transformation　stress　and　transformation　strain　for　polycrystalline　NiTi　under　tension　and　compression　is　proposed.　The　model　defines　three　crystallographic　regions:　tension-favorable,　compression-favorable　and　neutral　zones.　The　orientation　population　in　which　tensile　strains　are　larger　than　compressive　strains　is　much　higher　than　that　of　orientations　with　higher　compressive　strains.　For　resolved　shear　stress,　orientation　populations　favoring　tension　and　compression　do　not　show　any　great　difference.　(C)　2010　Acta　Materialia　Inc.　Published　by　Elsevier　Ltd.　All　rights　reserved.