The doctoral thesis presents the finite element formulation for the analysis of spatial and planar layered beams. The designed finite elements are based on Reissner geometrically exact theory to model the individual layers. Through quaternion parametrization of the rotations, we avoid singularities, by assuming constant deformations along the length of a finite element, the need for interpolation, and the choice of deformation quantities as primary unknowns, the effect of shear blocking. The robust, adaptive, mathematically consistent and singularity-free computational model also includes a distributed system of nonlinear springs to describe the connection between the layers. Since the interfaces can be described by any function of spring stiffness, the model is able to consider various physical phenomena such as friction between layers, contacts, cohesion forces, etc. Thorough tests on thick solid beam, thick partially delaminated beam, overlap shear test and film-substrate composite demonstrate the efficiency and versatility of the proposed numerical method. The comparison of our results with those of the literature and commercial finite element analysis software shows the advantages of the proposed formulation, especially when the structure is subject to large shear deformations. This is due to the fact that our model provides a mathematically consistent method for iterative updating of all variables describing the beam.