The selection of the diaphragm constitutive model is directly related to the precision of hot diaphragm forming simulation. In order to analyze the applicability of five hyperelastic constitutive methods to different diaphragm materials, uniaxial tensile tests were carried out on two different types of diaphragm materials (nylon diaphragm and silicone rubber diaphragm) at different temperatures, and the performance differences of the two types of materials were analyzed by stress-strain curves, fracture elongation, and modulus. Five hyperelastic constitutive models were used to fit the data of diaphragm materials in the uniaxial tensile tests, and the data were compared with the simulation data of the uniaxial tension and hot diaphragm forming process of the diaphragm materials. The results indicate that the rubber diaphragm material has a greater fracture elongation than the nylon diaphragm, but its modulus is much smaller than the nylon diaphragm material. The Ogden, Polynomial (N = 2), and Marlow models have a high degree of fit for uniaxial tensile data of nylon and rubber diaphragms. However, the Yeoh model has a low degree of fit for uniaxial tensile data of nylon diaphragms but a high degree of fit for rubber diaphragms. Mooney-Rivlin model fails to accurately reflect the stress-strain relationship of hyperelastic material under large deformation, and the degree of fit of uniaxial tensile data of two diaphragm materials is relatively low. The Ogden and Polynomial (N = 2) models established based on uniaxial tensile data exhibit excessive stiffness during the simulation of hot diaphragm forming, while the Marlow model has high prediction accuracy.