Thin-shell structures, widely used in mechanical and civil engineering, are prone to geometric instabilities such as buckling and warping. The objective of our work is to analyze the dynamic instabilities of thin-shell structures by developing 3D-shell elements based on Mindlin-Reissner kinematics which incorporates the concept of EAS (Enhanced Assumed Strain, [1]). EAS field corresponds to an incompatible strain, controlled at the element level by an orthogonality condition in order to alleviate locking issues [2]. Dynamic buckling analysis is first conducted using a conventional technique such as the Newton-Raphson (NR) method in implicit dynamics. Then the reference NR method is compared to the Asymptotic Numerical Method (ANM) based on the Taylor series expansion (or Padé approximants) of an introduced homotopy parameter ε, applied to the quadratic non-linear terms in the discrete governing equations [3, 4]. For each loading step, the ANM establishes a sequence of linear problems that admit the same tangent matrix, thus reducing the computation time compared to the NR method, which updates the tangent matrix at each iteration. The 3D-shell with 7-parameters element has been reformulated into an updated Lagrangian formulation in order to implement the strategy proposed by [5], so as to integrate elasto-plasticity in finite strain. In implicit dynamics, the NR method has been validated with geometric and material non-linearities for numerous buckling quasi-static and dynamic buckling cases [6, 7]. Explicit solvers are also explored: in addition to the classic Central Difference scheme, we propose an explicit multi-time step solver based on Heterogeneous Asynchronous Time Integrator (HATI) methods [8, 9, 10]. Furthermore, an original treatment of the orthogonality condition for the EAS field is proposed, enabling the efficiency of explicit solvers to be preserved. Finally, due to the very general framework in which the implicit and explicit solvers are developed, various subdomain spatial discretizations are considered, as well as their coupling via mortar methods. For instance, implicit and explicit calculations are validated for a thin-shell structure, decomposed into subdomains using different types of element, non-conforming meshes and different time step sizes: the mesh combines quadratic (quadrangular and triangular) shell elements, spectral shell elements with Lagrange polynomials (degree 4), and finally full-3D 20-node hexahedral elements.