Due to the unique structure of tensile sheet specimens with a circular hole (CHS specimen), a novel method is proposed to predict the large-range uniaxial stress-strain relations of elastic-plastic materials analytically. Based on the energy equivalence principle, a load-displacement semi-analytical model of the CHS specimen is proposed. Subsequently, a semi-analytical model of constitutive parameters of elastic-plastic materials is developed by virtue of the load-displacement relation of the CHS specimen, and the prediction of the material’s stress-strain relations is obtained. To examine the validity of the models, numerical simulations with a series of materials were performed. The results demonstrated that the dimensionless load-displacement curves and stress-strain relations obtained using the proposed models correspond well with those obtained using finite element analysis. In addition, tensile tests were performed on the CHS specimen for four elastic-plastic materials (T225 titanium alloy, 6061 aluminum alloy, Q345 steel, and 3Cr13 steel), and the validity of the models is also verified by the experimental results. Compared with the conventional uniaxial tensile tests, the stress-strain relation of elastic-plastic material captured by the novel method corresponds to a larger strain, which is of great importance for engineering design and safety assessment.