This paper studies the shiftability of the face dog clutch with chamfered teeth. The effect of the chamfer angle on the shiftability map and the probability are studied. In contrast to previous studies, a generalized mathematical model is developed based on the shiftability condition. The analysis considered two sets of cases: the overlap distance cases, and the chamfer side cases. The overlap distance cases locate the successful engagement position. The chamfer side cases investigate the effect of the system geometry and consider two cases. The results show that the chamfer angle has a negative effect on the dog clutch shiftability. Some geometric parameters show a different effect on the engagement probability for the rectangular tooth and chamfered tooth cases, and this behaviour is also analysed.