Drilling is the most frequently employed operation of secondary machining for fiber-reinforced materials owing to the need for structure joining. Delamination is one of the serious concerns during drilling. Practical experience shows that an eccentric twist drill or an eccentric candle stick drill can degrade the quality of the fiber reinforced material. Comprehensive delamination models for the delamination induced by an eccentric twist drill and an eccentric candle stick drill in the drilling of composite materials have been constructed in the present study. For an eccentric twist drill and an eccentric candle stick drill, the critical thrust force that will produce delamination decreases with increasing point eccentricity ξ. The results agree with industrial experience. The need for control of drill eccentricity during drill regrinding has been proved analytically by the proposed models.