In this study, an overview is taken of the currently used beam and plate theories in the field of sandwich structures. Most of these models have several imperfections in the sense of physical correctness. Particularly, the boundary conditions of zero shear stresses on the free surfaces are not satisfied and the continuity of the shear stresses between layers is not ensured for laminated structures, too. On the other hand, the continuity conditions between the intact and delaminated regions are also not obvious. Shear stresses have an important role from the fracture mechanical point of view in calculating the energy release rate at the crack front, therefore, this investigation is required and necessary. This research aims to present new models and methods for analysing delaminated sandwich structures. On the first hand, Reddy's third-order theory can be improved for a layerwise analysis with a compressible core layer that fulfils all the boundary and continuity conditions. Furthermore, the well-known higher-order theories can be complemented with auxiliary conditions which may be added to the model by the Lagrange multipliers. In both cases, there are no general analytical solutions for these models. Hence, numerical methods should be applied to solve these problems. Here, two ways will be discussed for creating numerical models. Firstly, classes of special finite elements are created by the corresponding theories. Lagrange multipliers can also be treated by finite element approach. On the other hand, the governing differential equations may be discretized as well. An effective way to do discretization is the differential quadrature method which is a really convenient procedure for solving boundary value problems. Throughout this study, the previously mentioned models and methods are subjected to a comprehensive comparison.