Mechanical properties of biodegradable poly(butylene succinate-co-terephthalate) (PBST) fibers with 70 mol% butylene terephthalate (BT) were intensively investigated. Chemical structure composed of hard BT units and soft butylene succinate (BS) units made contributions to the higher elongation at break and lower initial modulus of PBST fibers than poly(butylene terephthalate) (PBT) fibers. Moreover, PBST fibers had better elastic properties than PBT fibers by exploring their elastic recovery. The stretch elastic recovery mechanism of PBST fibers was clarified from the point of crystal structure transition. According to the preliminary studies by wide angle X-ray diffraction (WAXD) measurements, two polymorphs (${alpha}$ form and ${eta}$ form) were confirmed when PBST fibers were applied to different deformations. With the help of intensive study by small angle X-ray scattering (SAXS) measurements, the crystal structure transition of PBST fibers was further verified.