A number of geophysical observations reveal that the underthrusting Indian continental plate beneath the southern Tibetan Plateau is laterally torn and segmented, with contrasting subduction angles along strike. However, the mechanism of such kind of slab tearing remains unclear. Here, a series of 3‐D high‐resolution numerical models are conducted, which suggest that the lateral variation (either gradually or abruptly changing) of boundary convergence rate plays a critical role in the tearing of underthrusting continental slab. The abruptly changing convergence with a large lateral contrast could lead to slab tearing all by itself, whereas the gradually changing convergence should be combined with pre‐existing weakness in the underthrusting block. The structures and properties of overriding block play secondary roles. Finally, we propose that Indian slab tearing could be attributed to the time‐dependent and lateral variation of convergence rate during the Indian‐Asian collision and the pre‐existing Indian lithospheric weakness. Plain Language Summary Horizontal slab tearing associated with the final slab break‐off occurs in many places of the global subduction‐collision system, the mechanism of which is easier for understanding and is mainly driven by the negative buoyancy of the subducted slab. However, for the underthrusting Indian continental plate beneath the southern Tibetan Plateau, the slab tearing and fragmentation occurs along several vertical planes perpendicular to the collision zone, which is identified by a number of geophysical explorations. It is rather difficult for a coherent subducting slab to tear along these sub‐vertical planes due to the lack of major forces in the along‐strike direction. Thus, the mechanism of Indian slab tearing is widely debated and remains unclear. In this study, many speculations have been tested by conducting a series of 3‐D high‐resolution numerical models. The model results indicate that the Indian slab tearing may be resulted from the time‐dependent and lateral variation of convergence rate between the Indian‐Asian collision and the resulting rotation of Indian continent, as well as the pre‐existing weakness within the Indian plate. Alternatively, the structures and properties of overriding Tibetan plate only play secondary roles. Key Points Systematic 3‐D numerical models are conducted to study the mechanism of Indian slab tearing along vertical planes beneath Tibetan Plateau Lateral variation of boundary convergence rate (either abruptly or gradually changing) is generally required for such slab tearing Indian slab tearing may be attributed to the gradually changing collision rate along strike and the pre‐existing lithospheric weakness