In the present paper, the nonlinear response that arose during unloading under compression of a rolled magnesium alloy sheet was investigated using a crystal plasticity finite-element method, focusing on the effects of twinning and detwinning. The mechanism that the nonlinear response was more pronounced under compression than that under tension was also discussed. In the simulation, a twinning and detwinning model that had originally been proposed by Van Houtte (1978) and recently extended to the detwinning process by the present authors [Hama and Takuda, 2012] was employed. From numerical experiments, it was confirmed that, as already pointed out in previous studies, the activity of detwinning played an important role in the nonlinear response during unloading. On the other hand, it was also found that the nonlinear response under compression was still larger than that under tension when the detwinning was not taken into account in the simulation. These results indicated that there would be other factors that induce the more pronounced nonlinear response under compression than that under tension. Copyright © 2013 Trans Tech Publications Ltd.