A mathematical model is presented to study the motion of the spermatozoa in the cervical canal by considering the transverse waves along its tail and the transverse and longitudinal motions of the cervical wall. In an attempt to control fertility by reducing the speed of sperm, the transverse waves have been considered in the direction opposite to the motion of the spermatozoa. It has been shown that by having appropriate transverse wave motion and longitudinal velocity, the sperm may not be able to move towards the oviduct even if it could continue to have its own propelling velocity. A particular case of the motion of a thin plane sheet in a channel under peristaltic motion of its walls has also been obtained and studied.