A Zn-Al eutectoid alloy known as a fine-grained superplastic material is tested both in tension and compression under superplastic conditions, and the influence of the stress state on superplastic deformation behavior, such as flow stress, is investigated. In the compression test, deformation is interrupted and turning is performed to remove a barreled portion so that the gauge section becomes uniform, and then the deformation is continued. Microstructural change during the deformation is also investigated. As a result, flow stress in the compression becomes higher than that in tension even after the barreled portion is removed. After deformation, grain growth is observed both in the tension and compression, and growth rate in the compression is larger than in the tension.