Composites have become valuable construction materials in the aerospace, defense, automobile, and civil industries due to their superior mechanical properties. However, there are significant differences between the machining of metals and alloys and that of composites, because composites are anisotropic and inhomogeneous. Drilling with a conventional twist drill is characterized by a relatively large thrust force due to a negative rake and negligibly small cutting speed at the chisel edge. Such a large thrust force causes defects and damages the composites, leading to poor hole quality, and reduced in-service life under fatigue loads. Although significant efforts have been made to realize the thrust force of twist drill, there are few papers reporting the effect of peripheral drilling moment (torque) on delamination in drilling composite materials. In this paper, an attempt is made to develop the critical thrust of the twist drill with peripheral drilling moment using linear elastic fracture mechanics (LEFM) and energy conservation. The theoretical results agree well with the practical experience in industries.