This thesis presents new numerical models for analysis of thin beam and arch structures and thin plate and shell structures based on the combined finite-discrete element method (FDEM). The new models perform quasistatic and dynamic analysis. The thesis also presents an overview of the established numerical tools for the analysis of arch and shell structures, together with their strengths and disadvantages. The bases of the combined finite-element method and its strengths are also presented. The main motivation was the development of precise, robust and computationally efficient numerical models. The model for the analysis of thin beam and arch structures uses straight two-noded rotation free finite elements, and takes into account linear-elastic material behaviour, finite displacement, finite rotations and small strains. The thesis describes axial and bending carrying mechanisms of a beam finite element in detail. The presented model is implemented into the open source FDEM package ‘Yfdem’. Performance of the new numerical model is demonstrated on simple benchmark tests by a comparison with known analytical and numerical results. Its application for the seismic analysis of arch structures is presented. This thesis also presents a new numerical model for analysis of thin plate and shell structures. The model uses three-noded triangular finite elements, and takes into account linear-elastic material behaviour, finite rotations, finite displacements and small strains. The thesis describes membrane and bending carrying mechanisms for triangular finite element in detail. The model is implemented into the open source FDEM package ‘Yfdem’. Performance of the new numerical model was demonstrated on simple benchmark tests by comparing it with the known analytical and numerical results. Its application in typical problems of stability of plate and shell structures is presented. Directions for further development and upgrade of the model in performing contact interaction and material nonlinearity are given.