The presentation of the finite element method starts in this chapter with the explanation of the finite element method for truss and beam systems. The concept of stiffness matrices is shown first for a simple truss element. The procedure for setting up the equations for a finite element analysis is explained exemplary for a simple truss system. The procedure itself, however, is not limited to truss systems, it can be applied to other finite element systems as well, consisting of beam, plate and solid elements. The next sections deal with springs and with beam elements subjected to bending and their mechanical background. Two- and three-dimensional truss and beam systems are treated. It follows an extensive discussion of the modelling of beam structures. Symmetry conditions to be used for symmetrical structures are discussed as well. The chapter ends with some aspects of error sources including numerical errors and of the quality assurance of finite element analyses.