Lithium-ion pouch battery (LIPB) is widely applied in different engineering fields, such as electric vehicles, aeronautics, astronautics, and among others. However, few complete mechanical models with deformation field are presented to predict internal short circuit (ISC) and resistance exterior force property of LIPB under exterior loading. In the present research, the indentation theoretical models with sinusoidal shape function are established to investigate resistance exterior force property of batteries with different positive materials under different punch shapes loading. The effects of indentation displacement and deformation region on indentation force are carried out. By the comparison of indentation force, present theoretical and numerical results are consistent with previous experimental results. The indentation force increases with the punch radius increase, but decreases with the indentation displacement increase. On the basis of energy conservation law, it is concluded that LIPB is more likely to produce mechanical failure and ISC when normalized deformation region is greater than or equal to 0.4 and plastic strain energy ratio is greater than or equal to 1.5. In addition, from resistance exterior force property point of view, LIPB has a better property to resist external force when LiMnNiCoO2, rather than LiCoO2 and Nanophosphate, is used as positive material. The research provides a reference for assessing the safety of LIPB and selecting suitable positive material, which possesses high energy capacity and resistance exterior force property.