During drilling CFRP composite plates, the direction pointing to the hole wall along the length can be considered the forward direction of the carbon fiber. The angle between the forward direction of the cutting speed and the forward direction of the carbon fiber is regarded as the main cutting angle of the major cutting edge. If the main cutting angle is an acute angle, the cutting is called as forward cutting. If the main cutting angle is an obtuse angle, the cutting is called reverse cutting. From the above concepts, the forward cutting zone and the reverse cutting zone can be defined. Based on viscoelastic mechanics and foundation beam theory, the carbon fiber among CFRP composite plate is regarded as an infinite or semi-infinite foundation beam with equal section on elastic foundation. The calculation model of equivalent stiffness modulus is derived, and the thrust force model of the major cutting edge is established. The research shows that when the drill bit turns for a revolution, the forward cutting and reverse cutting alternately change twice, and the main cutting angle and thrust force of the major cutting edge change 2 cycles. The cutting mode of the major cutting edge is the fundamental reason which brings about the periodic change of the thrust force and the defects of the entrance or exit. The reliability of the thrust force model of the major cutting edge is proved by drilling experiments. This study can provide theoretical support for improving the drilling process of CFRP composite plates.