The use of sandwich structures increases rapidly for applications ranging from satellites, aircraft, ships, automobiles, rail cars, wind energy systems, and bridge construction. One challenge in these applications is to understand in detail how different damages influence the structure and what their behavior in-service is. The traditional numerical simulation methods have constraints in machine-resource savings, and this leads to difficulties in the local effects study. Thus the new efficient methods and tools for simulation need to be developed and adjusted. Firstly, the work is developed in the analytical study of kinematic models. Many investigations have been devoted to the static and dynamic analyses of these structures and various theories and models have been proposed on the base of two-dimensional modelling of multi-layered plates and shells, such as the Classical Laminate Theory, CLT, the First-order Shear Deformation Theory, FSDT, the Higher-order Shear Deformation Theories (HSDT) and the Zig-Zag theories. Secondly, a multiscale method based on Arlequin approach is proposed to study local effects in sandwich structures. The Arlequin method offers a framework to mix and glue different models with others. In our work, a new coupling operator is developed for sandwich beams, quantitative tests are presented in different linear examples. Thirdly, the combination, between the Arlequin method and the Asymptotic Numerical Method (ANM), is realized in the nonlinear application which consists in the local buckling analysis of sandwich structures. The ANM is an alternative method which falls into the category of perturbation techniques.