In this paper, the mechanical properties of the fibers made from multifunctional copolyester and PET have been investigated. The results showed that the rebound resilience and the dimensional stability of the copolyester fiber were better than that of PET, under the constant elongation, the internal stress of the copolyester fiber was higher than that of PET, and the relaxation process of the internal stress about the copolyester fiber bore analogy to that of PET.