In this paper, the injection process of glassy nuclear waste is simulated using the ANSYS Workbench simulation platform and the birth and death element method. The results show that the temperature change trend obtained by simulating the injection process of solidification container by using the birth and death element method is consistent with the literature results. It is feasible to simulate the injection process of glassy nuclear waste by using the birth and death element method of ANSYS. The thermal calculation results show that the container above the liquid level will produce large stress due to mutual restraint, and the container will undergo plastic deformation when heated during the injection process. As the pouring temperature increases from 1000°C to 1200°C, the maximum stress at the upper head increases from 212.88 to 232.46 MPa. The deformation degree of the solidified container increases with the increase of pouring temperature during the injection process. With the increase of pouring rate from 0.025 to 0.04 kg/s, at the end of injection, the maximum stress of the upper head decreases from 226.96 to 214.71 MPa with the increase of pouring rate. The overall deformation degree of the solidified container increases with the increase of the pouring rate.