A micromechanical model of cross-over fiber bridging is developed for the prediction of macroscopic mixed-mode bridging laws (traction-separation laws). The model is based on non-linear beam theory and takes into account debonding between fiber and matrix as well as buckling of fibers in compression. Further, it is shown how failure of the bridging fibers can be taken into account through a Weibull distributed failure strain. Predictions made by the proposed model are compared with predictions made by detailed 3D finite element models, and a very good agreement was observed. It is shown that models based on linear beam theory are only valid for small transverse deflections of the bridging ligament and greatly underestimate the force transferred by ligaments subjected to moderately large deflections. The novel model, on the other hand, is applicable in the entire range where the bridging problem transitions from a beam bending problem to a bar-like problem. Finally, an example of how the proposed model can be used for parameter/sensitivity studies is given. A conclusion from this study is that reducing the fracture toughness, Gc, of the interface between fibers and matrix may lead to increased energy dissipation through cross-over fiber bridging as more fibres remain intact longer.