An effective computational model is required to accurately predict the dynamic responses in accidental initiations of explosives. The present work uses a series of two-dimensional mechanical-chemical simulations performed via a hydrodynamic-code, DREXH-2D, to efficiently describe the mechanical and ignition-deflagration responses of cased cylindrical polymer-bonded explosives (PBXs) undergoing a low to-medium-level impact (70-350 m/s) in longitudinal direction. The ignition response was predicted based on an ignition criterion of effective plastic work. Slow burning and its growth to deflagration were described through a pressure-dependent reaction rate equation. The extreme value of effective plastic work was found to be useful to determine the ignition threshold velocity for PBXs. For low-level velocity impact, the incident stress wave reflection from lateral surfaces contributed to the formation of ignition regions. After the ignition, the deflagration was induced in the medium-level impact, and its violence was related to the shock strength. However, the low-strength stress wave only induced reaction at local regions, and sequent burning was no longer sensitive to the strength of incident wave. The predicted pressure and temperature results of PBXs were consistent with the medium-level impact tests performed by China Academy of Engineering Physics. (C) 2017 Elsevier B.V. All rights reserved.