Parachutes and other inflatable aerodynamic decelerators usually use flexible fabrics due to their lightweight and high load-carrying capacity. The behavior of fabrics during complex deformations is mainly influenced by their shear properties. The shear properties of fabric can be explained by the shear stiffness or shear modulus. The design optimization of these inflatable structures relies on a detailed knowledge of the mechanical properties of the fabric material. To investigate the effect of shear modulus on the inflatable shapes of parachute canopies, an arbitrary Lagrangian–Eulerian coupling method based on the incompressible computational fluid dynamics solver and structural solver LS-DYNA is proposed. Finite element methods are used to describe continuous materials such as fabrics and airflow fields. The effects of the shear modulus on the inflated parachute shapes are investigated from the macroscopic and microscopic scales. A comparison analysis reveals that different shear moduli have little effect on the overall shape and in-plane shear strain of the parachute, while they have significant effects on the in-plane stress distribution and wrinkles of the parachute. The methods and conclusions of this paper can provide some reference for the materials design of parachutes in preforming stage.