The deformation behavior of sheet metal is currently presented by the stress-strain curve, which gives the variation of flow stress as strain increases. The correlation between stress and strain is also used to characterize the material hardening under different stress states. For anisotropic materials, the deformation behavior depends on stress state, and it is important to realize similar deformation conditions to obtain the stress-strain relationship. In this article, the profile of the free bulging zone was described by a tangent circle model during tube bulging test with fixed ends. In conjunction with the newly suggested linear-model for instantaneous thickness at the middle point, an analytical model and testing method is developed to establish the equivalent stress–equivalent strain relation of tubes. Experiments of STKM11A steel tube have been carried out, and different yield criteria are adopted to define the equivalent stress and equivalent strain. The effect of the anisotropic parameters on the mechanical property is analyzed. Results show that the profile of the free bulging zone can be well reproduced by the tangent circle model for practical application, and the analytical model and data measuring method for the bulging test can be simplified. The equivalent stress–equivalent strain curve by bulging test is rather different from that by uniaxial tension test, with a lower equivalent stress in the initial yielding stage and a greater rate of the equivalent stress increasing with the increase of the equivalent strain. In addition, the shorter the bulging zone length is, the greater the maximum equivalent strain is, because equal-biaxial stress state is approached. As the axial stress is significantly smaller than the hoop stress in bulging test, the anisotropic parameter along the hoop direction has a stronger effect on the determined curve and should be determined precisely.