For a cold-rolled NiTi sheet, the tensile stress-strain curves show a flat stress-plateau during tension along the rolling direction, while under tension along the transverse direction the specimens are quickly strain-hardened and no flat stress-plateau occurred. This shows that the deformation mechanisms of martensite twins are different when loading along different directions. TEM observations show that, in the as-annealed condition, the major type of twins in the martensite phase is  type II twins in the present material. Also present are (001) compound twins and a small amount of (11 (1) over bar) type I twins. Deformation details of these three types of twins are different along rolling and transverse directions. After deformation along the rolling direction to 6% strain, reorientation and de-twinning of the  type II twins have occurred, while after deformation along the transverse direction to 6% strain, no significant reorientation and de-twinning of  type II twins have been observed. Instead, a high density of dislocations has been generated inside the  type II twins and de-twinning of the (001) compound twins has been observed. A further crystallographic analysis shows that the shear direction of each type of martensite twins relative to the loading direction is different, which may explain the different deformation behaviour of the twins. This may also account for the macroscopical deformation behaviour of the material. (C) 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.