Flat-scored metal diaphragms are essentially used in various hypersonic impulse facilities as quick-opening valves. Their burst pressure is a key parameter to optimize the performance of shock wave experimental devices and ensure the activation of overpressure safety devices. However, the conventional method to predict the burst pressure relies on time-consuming experiments that pose significant challenges for ultrahigh driving conditions. In this study, the finite element method (FEM) based on the Johnson-Cook model is adopted to predict the burst pressure of diaphragms used in a shock tube. The influences of the diaphragm thickness and groove depth on the burst pressure are analyzed. A simplified approximation based on the simulation results is obtained to estimate the burst pressure under a static load rapidly. This method is more generalizable than the existing equation and produces results in good agreement with experimental results. Furthermore, the burst pressure is investigated under different dynamic loads using the proposed FEM method. The results show that the dynamic load results in larger burst pressures than the static load, indicating that the burst pressure depends on the load type, the loading rate, and the magnitude of the applied forces.