Recent anatomical studies of extraocular muscles (EOM) demonstrate the stability of muscle paths. This is due to the fact that each rectus EOM passes through a pulley consisting of an encircling ring or sleeve of collagen. In this paper, the EOMs are modeled using the Hill type musculotendon complex and the effect of extraocular pulleys are studied. The model proposed by Martin and Schovanec in 1999, for horizontal eye movement has been used as a basic starting point. The extraocular pulleys are then introduced and analyzed mainly to study how Listing's law is enforced and how it implements an oculomotor plant which appears commutative to the brain.