Biodegradable poly(butylene succinate-co-cyclohexanedimethylene succinate) (PBCS) was synthesized via polycondensation. The composition of PBCS was characterized by H-1-nuclear magnetic resonance (H-1-NMR). By incorporation of 20 wt% of cyclohexanedimethylene succinate, stress oscillation behavior in stress-strain curve was observed during cold drawing. The stress was no longer stable, but exhibited constantly periodic fluctuations. Morphology and crystalline structure of oscillatory portion were evaluated by scanning electron microscopy, and X-ray diffraction (XRD), respectively. The melting behavior was studied using differential scanning calorimetry (DSC). The surface morphology of oscillatory portion presented alternating opaque and transparent bands, which were perpendicular to the cold-drawing direction. By comprehensive analysis of stress-strain curve, surface morphology, XRD, and DSC, the formation of stress oscillation was discussed. To describe stress oscillation, a new mathematical model was proposed to simulate stress oscillation and its viscoelastic behaviors were well explained. The novelty of the mathematical model was that new oscillatory cells consisting of a dashpot with free inextensible strings were adopted to instead of fiber bundle cells. POLYM. ENG. SCI., 55:966-974, 2015. (c) 2014 Society of Plastics Engineers