Soft fibrous materials are widely used in engineering applications, particularly in the biomedical field, where they are increasingly employed in tissue engineering and regenerative medicine due to their ability to mimic the architecture of the extracellular matrix of soft tissues and to promote cell infiltration. Among the most important mechanical requirements for such materials is the ability to maintain structural integrity under hemodynamic loading, as premature crack initiation and fatigue failure can otherwise occur. Despite this relevance, the understanding of crack propagation in soft fibrous materials, which are characterized by nonlinearity and strong anisotropy, is still incomplete, leading to a lack of standardized models. Our experimental investigations on electrospun polymer networks revealed a strong dependence of the crack propagation direction on the material’s preferential fiber orientation. Under pure shear loading, kinking of the existing crack occurred. To predict the fracture resistance of these materials, we present a numerical framework based on configurational forces and a virtual crack increment. This method serves to determine the crack kinking direction based on the criterion of maximum energy release rate. The proposed method was validated using standardized specimens in linear elastic fracture mechanics as well as on hyperelastic isotropic and anisotropic materials. The combined experimental and computational approach provides a robust framework for assessing the fracture and fatigue properties of nonwoven fibrous materials.