A second gradient theory for woven fabrics is applied to Kirchhoff–Love shell elements to analyze the mechanics of fiber reinforced composite materials. In particular, we assume a continuous distribution of the fibers embedded into the shell surface, accounting for additional in-plane flexural resistances within the hyperelastic regime. For the finite element discretization we apply isogeometric methods, i.e. we make use of B-splines as basis functions omitting the usage of mixed approaches. The higher gradient formulation of the fabric is verified by a series of numerical examples, followed by suitable validation steps using experimental measurements on organic sheets. A final example using a non-flat reference geometry demonstrates the capabilities of the presented formulation.