Orthogonal cutting of unidirectional fiber-reinforced polymer composites was analyzed using the finite element method. A dual fracture process was used to simulate chip formation incorporating both the maximum stress and Tsai-Hill failure criteria. All aspects of the cutting tool geometry are considered in the model including the tool rake and clearance angles, nose radius and wear land, as well as friction between the tool and work material. Predictions for the cutting forces from numerical simulations are verified with experimental measurements for orthogonal trimming of unidirectional graphite/epoxy. The principal cutting force predictions agree very well with those obtained from experiments. The influence of fiber orientation and tool geometry on the fracture stress are highlighted and their effects on the material removal process in orthogonal trimming of reinforced polymers are discussed.