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LFRP (Long Fiber Reinforced) composites are widely used in structural components for high responsibility applications in different industrial sectors. Composite components are manufactured near final shape, however several machining operations are commonly required to achieve dimensional and assembly specifications. Machining should be carefully carried out in order to avoid workpiece damage. Despite of the interest of numerical modeling to analyze in detail the phenomena involved during composite cutting, there are only few works in the scientific literature dealing with this topic even in the simple case of orthogonal cutting. Out-of-plane failure can be accounted only if three dimensional modeling is performed. However up to date numerical analysis of cutting found in scientific literature was focused in two-dimensional approach. In this paper (2D) and three dimensional (3D) numerical modeling of orthogonal cutting of carbon LFRP composite are presented. The aim of the paper is to analyze the complex aspects involved during cutting, including out-of-plane failure.