Fabrics are an extremely important element of body armors and other armors. Understanding fabrics requires understanding how yarns deform. Classical theory has shown very good agreement with the deformation of a single yarn when impacted transversely. However, the impact speed at which a yarn breaks based on this classical theory is not correct; it has been experimentally noted that yarns break when impacted at a lower speed. This paper explores the mechanism of yarn breakage. The problem of the transverse strike of a yarn by a flat-faced projectile is analytically solved for early times. It is rigorously demonstrated that when a flat-faced projectile strikes a yarn, the minimum impact speed that breaks the yarn will always be at least 11% less than the classical-theory result. It is further shown that when the yarn in front of the projectile “bounces” off the projectile face due to the impact, the impact speed that breaks the yarn is further reduced. If the yarn bounces elastically off the projectile face at twice the impact velocity (the theoretical maximum), there is a 40% reduction in the projectile impact speed that breaks the yarn.