In this paper, specimens of a new kind of envelope material for the stratospheric airship with and without initial notches are tested under uniaxial and biaxial tensile conditions. It can be seen from the tests that the characteristics of nonlinearity and anisotropy are not so obvious, especially for the biaxial specimens. The damage process of the on-axial specimen is brittle failure, because the damage of the specimen takes place suddenly without any distinct phenomenon, and there is no obvious yield stage before the failure of the material. The failure strength and the damage mode of the envelope material are determined by the strength of the woven fabric and the off-axial angle, respectively. The simplified maximum stress criterion and a new modified Tsai-Hill criterion can be used to predict the failure of the envelope material under on-axial and off-axial tension, respectively. The results show that it is the number of the cutoff yarns but not the shape of the initial damage determines the failure strength of the envelope material. In addition, the stress concentration factor of the envelope material is much higher than the isotropic material, because of the difficulty to transfer concentrated stress around the initial opening hole.