The trapezoid tearing behavior and damage mechanism of envelope materials were investigated. Numerical simulation studies were conducted on a typical warp-knitted envelope fabric under a series of parameters, considering the microscopic structure of the yarns and the nonlinear characteristics of the envelope material. First, the numerical simulation method was verified by comparing the obtained results with experimental data. Then, the damage morphology and tearing damage process under typical bias angles were analyzed by the numerical simulation results. Next, the effects of the slit length and bias angle on the mechanical behavior and tearing strength of the envelope material were discussed in detail. Finally, the shearing effect was introduced and the prediction theory of off-axis trapezoid tearing strength of envelope material was proposed. Results show that the shape and extent of the airfoil-shaped stress concentration zone in the vicinity of the slit were vital factors influencing the propagation direction and tearing strength of slit. The evolution of the airfoil-shaped zone of stress concentration was obviously affected by the slit length and initial bias angle of yarns. Slit length could interfere with the out-of-plane deformation of envelope surface, the shape of slit tip, and the stress level of yarns. As the slit length increased, the fracture displacement decreased significantly, whereas the on-axis tearing strength increased. Since the yarn direction could exert complex effects on the airfoil-shaped zone and the stress level of the yarn, an inverted “V”-shaped relationship was presented between tearing strength and yarn bias angle. The research findings can provide reference for the slit arrest analysis and safety assessment of pneumatic membrane structures.