Due to the increasing demands for lightweight parts in various fields, such as bicycle, automotive, aircraft and aerospace industries, hydroforming processes have become popular in recent years. Since tubular materials during tube hydroforming are under a bi-axial even tri-axial stress state, which is different from that in the tensile test, it is necessary to test the mechanical properties of the material under bi-axial stress state. Tube bulging test is an advanced method for characterizing the mechanical properties of tubular materials under bi-axial stress state. But there are excessive physical quantities in the theoretical model of tube bulging test for testing the mechanical properties of tubes under bi-axial stress state which are difficult to be obtained during the experiment. In order to solve the problems, a method for directly testing the mechanical properties of tubes under bi-axial stress state was proposed in this work, which will be referred to as "one point method". Because of circular model is characterized by a dominant function expression, theoretical models of both the pole axial curvature radius and the pole thickness during bulging test are derived under supposing the geometrical models for bulging zone as circular. Thus, the mechanical properties of tubes under bi-axial stress state can be obtained only through measuring the bulging height at the pole point during the bulging test, which laid the foundation for the establishment of a simple and reliable method for testing the mechanical properties of the tube online. Based on the above proposed method, the extruded aluminum alloy tubes AA6061 were tested. The results showed that both the pole axial curvature radius and the pole thickness during bulging test can be expressed as display functions pertaining to the bulging height at the pole point. For the theoretical model of the pole axial curvature radius, as the bulging rate increases, the prediction accuracy increases at beginning, and decreases at the end when using circular as the theoretical geometrical models for bulging zone. The prediction accuracy is the highest as the bulging rate is about 13%, the prediction accuracy decreases after the bulging rate is more than 20%. Fortunately, the overall prediction error is small. The maximum error does not exceed ±0.9%. The prediction accuracy of the pole thickness using the theoretical model is almost unaffected by the specimen geometry. When the ratios of length to diameter and diameter to thickness change, the difference is very small, the prediction error is not more than 0.8%. This is very helpful to ensure the accuracy of mechanical testing under bi-axial loading conditions. Using the "one point method", the stress and strain components along the circumferential and axial directions can be simultaneously measured, this laid the foundation for further analysis of the anisotropic property impacting on the flow and subsequent yield under complex stress state.