Due to stress concentration at the edges, fiber-fiber bonds under load are known to fail gradually inwards from the edges. In this paper, we propose a failure mechanism for fiber-fiber joints under load, based on the peak stresses occurring at the bond edges. We have modeled the mechanical testing of individual fiber-fiber joints using a finite element method (FEM) framework. The model is based on experimental results of fiber-fiber joint strength tests designed to induce each of the three modes in fracture mechanics: opening, sliding, and tearing. A parametric study of the peak load at the edges of the fibers was carried out in order to identify a failure mechanism. The peak stresses were not directly taken from the FEM models, as these values are highly discretization-dependent. Instead, the peak stresses were estimated from resultant forces and moments in the bond and an idealized geometry of the bonding region. The literature has, up to now, focused on shear load as a failure mechanism for fiber-fiber bonds. However, our findings indicate that pulp fiber joints are sensitive to normal stresses and insensitive to shear stresses. Hence, we suggest utilizing failure criteria related to normal stress in future work.