The theory of elastic shells is one of the important branches of the theory of elasticity. In this talk, we discuss several kinds of elastodynamic shell models, i.e., the time-dependent Koiter model, the time-dependent generalized membrane model, the time-dependent elliptic membrane model and the time-dependent flexural model, which have not been addressed numerically. We propose space-time full discretization schemes for several models. The corresponding analyses of existence, uniqueness, stability, convergence and priori error estimates are given. Finally, we provide numerical experiments with several kinds of shells to demonstrate the efficiency of models and the stability and convergence of numerical schemes.