Abstract: The non-coaxiality between the major principal stress and the principal strain increment directions is found to be an important feature of granular materials. The conventional constitutive models are based on the theory of coaxiality without considering the effect of non-coaxiality. A hollow cylinder apparatus is used to investigate the non-coaxiality between the axes of the major principal stress and principal strain increment and the effects of loading history on the degree of non-coaxiality. Two series of drained tests are carried out on Portaway sand. In the first series, the specimens are sheared along the fixed principal stress directions. In the second one, the specimens are compressed along the vertical direction before shearing along the same paths of the first series. The results show further evidence of the non-coaxiality. The degree of non-coaxiality has dependence on the loading directions as well as the effect of loading history. It is also found that the degree of non-coaxiality will reduce when the specimen approaches failure.