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This work is focused on the study of orthogonal cutting of long fiber composites. A model based in finite element was developed. The mechanisms of chip formation of Glass and Carbon Fiber Reinforced Polymer (FRP) composites were analyzed. Significant differences were observed when comparing machining induced damage predicted with the model for both materials. While damage extended widely ahead the interface and beneath the tool tip in the case of GFRP, damage was located in a much smaller zone in the case CFRP. The fiber orientation influences both the mechanism of chip formation and the induced subsurface damage.