The orientation density function of the fibers in a yarn has been newly defined and derived for the ideal migration structure, in which the fibers migrate regularly and uniformly from the outside to the center of the yarn and then back to the outside. The ideal migration behavior has been expressed in the mathematical equation by introducing the parameter JM defining rate of migration. The relative initial modulus of the yarn having the ideal migration structure was calculated by using the orientation density function and compared with that of the idealized helical structure. The initial modulus of the yarn has been found to decrease with the increase of the degree of migration.