A transient-dynamics model based on the approximate Riemann algorithm is proposed for the failure analysis of a frangible composite canister cover. The frangible cover, manufactured with a traditional manual lay-up method, is designed to conduct a simulated missile launch test using a specially developed test device. Deformation of the cover's centre is determined using a transient-dynamics finite element model; failure pressure for the frangible cover is obtained based on a failure criterion and compared with simulated experimental results. Weak-zone position of the frangible cover has a significant effect on failure pressure compared to that of deformation of the cover's centre. With the same structure of the weak-zone, an increase in its height can first raise and then reduce the level of failure pressure of the frangible cover. Close agreements between the experimental and numerical results are observed.