The objective of this research was to study chip formation mechanisms in order to predict damage in the orthogonal machining of unidirectional polymer-matrix composites by experimentation and analysis. This study presents a new analytical formula, which is able to successfully predict the fiber orientations at which depth of machining damage is higher based on different cutting parameters and can be used to minimize machining damage by selecting proper fiber and matrix materials. Orthogonal cuttings were conducted by experiments and then compared to the developed theory. The variables that were presented for this research were tool geometry and fiber orientation.