Stress oscillation has been observed in a number of linear thermoplastic polymers during the cold-drawing process, where the polymers exhibit periodic self-excited oscillatory neck propagation. However, the origin of the mechanical stress oscillation process and its relationship with the crystalline morphology of the polymer are still under debate. In this work, we revisit the stress oscillation behavior by studying a semi-crystalline polyester, poly(butylene succinate) (PBS), a biodegradable polymer suitable for biomedical and packaging applications. Stress oscillation of PBS is observed when deformed at a range of elongation rates from 10 to 200 mm min-1, and the fluctuation magnitude decays as the deformation temperature increases from 23 to 100 °C. Periodic transparent/opaque bands form during necking of PBS, which consists of alternating regions of highly oriented crystalline zones and microcavities due to crazing and voiding, although the degree of crystallinity did not change significantly in the bands. Simultaneous small- and wide-angle X-ray scattering confirms that the alternating stress increases, as shown in the stress-strain curves, correspond to the appearance of the transparent bands in the sample, and the abrupt drop of the stress is the result of voiding during the neck propagation. The voiding and cavitation are ultimately responsible for the stress oscillation process in PBS. The in-depth analysis of this work is important in understanding and controlling the occurrence of instabilities/cavitation during polymer processing such as film blowing, biaxial stretching and injection moulding of biodegradable polymer materials.