The tearing response of sheets of nonwoven fiber material is investigated. It addresses the question on how notch length and notch geometry is related to the tearing strength and tearing processes. The system considered consists of elastic-brittle fibers connected by strong interfiber bonds. Fiber fracture is the only failure mechanism. For a random fiber orientation case, deformation of the unnotched specimen occurs by long-range fiber chains connecting the load inducing boundaries, and failure is by tearing the cross section. The strength of the notched random fiber sheets is well described by a net section criterion, independent of the notch geometry. For a fiber orientation with symmetry relative to the loading direction, tensile loading is transferred by formation of the X-shaped fiber chains centered in the specimen. The subsequent failure occurs along the fiber chain by shear. Thus, the tearing strength is independent of the notch depth in double-edge notched and single-edge notched specimens, when the presence of shallow notch does not disrupt the force chains in the model. As the notch disturbs the fiber chains, alternative shear failure path forms near the notch tip, leading to a dependence of failure strength on the notch geometry. Then, the failure strength of notched nonwoven networks is described by a shear strength and a notch geometry term.