AbstractThe hard roof in coal mines will induce strong pressure problems for the working face and the lanes, which will seriously affect the safe and efficient production of the mine. For these issues, our team developed a new technology of cutting hard roof by composite blasting. With the new technology, a penetrating process is key to the directionally cut roof. Thus, an arbitrary Lagrange–Euler method is proposed to calculate the penetrating process. In this method, it was taken that the Jones–Wilkins–Lee constitutive model, Johnson–Cook constitutive model, and Holmquist–Johnson–Cook constitutive model to build a numerical model, by LS‐DYNA software, of the process of the penetrating the hard roof. Finally, the following conclusions were obtained: (1) The velocity variation law of metal liner from head to tail is revealed. The speeds of the metal liner's head and tail are 3500 and 450 m/s, respectively. (2) The shape of the channel formed by shaped charge jets is like a funnel, whose mouth's depth and diameter are 33 and 49 mm, respectively. The funnel's narrow diameter is 7.5 mm. (3) With the increase of the channel depth, the rock damage area changes in three different states: slow increase, rapid increase, and linear increase. Then, a shovel‐shaped geometric model of rock damage zone is established, whose key size parameters in the model are given.