A multiphase finite element model using the commercial finite element package ABAQUS/EXPLICIT is developed for simulating the orthogonal machining of unidirectional fiber reinforced composite materials. The composite materials considered for this study are a glass fiber reinforced epoxy and a tube formed carbon fiber reinforced epoxy. The effects of varying the fiber orientation angle and tool rake angle on the cutting force and damage during machining are considered for the glass fiber reinforced epoxy. In the case of carbon fiber reinforced epoxy, only the effect of fiber orientation on the measured cutting force and damage during machining is considered. Two major damage phenomena are predicted: debonding at the fiber-matrix interface and fiber pullout. In the multiphase approach, the fiber and matrix are modeled as continuum elements with isotropic properties separated by an interfacial layer, while the tool is modeled as a rigid body. The cohesive zone modeling approach is used for the interfacial layer to simulate the extent of debonding below the work surface. Bulk deformation and shear failure are considered in the matrix for both the models and the glass fiber. A brittle failure criterion is used for the carbon fiber specimen and is coded in FORTRAN as a user defined material (VUMAT). The brittle failure of the carbon fibers is modeled using the Marigo model for brittle failure. For validation purposes, simulation results of the multiphase approach are compared with experimental measurements of the cutting force and damage. The model is successful in predicting cutting forces and damage at the front and rear faces with respect to the fiber orientation. A successful prediction of fiber pullout is also demonstrated in this paper.