This final thesis entitled "ENERGY METHODS IN THE ANALYSIS BEAM SYSTEMS” is divided into six chapters. Each chapter deals with one energy method used in the mechanicsof materials. The first part of the each subchapter is a short theoretical introduction to every method, and then in the second part few examples are solved. The first chapter briefly explains the role of energy methods in solving problems. The key concepts of potential energy and work are introduced. Castigliano’s second theorem is derived from the definition of potential energy as a function of generalized forces. It is important to emphasize that the presented form of Castigliano’s second theorem is valid only for the linear elastic problems. In the third chapter, the Mohr integral is presented and Vereshchagino’s rule is shown in order to prevent laborious integration procedures. The force method is often used in solving statically indeterminate systems. The forces and moments are unknowns, and the transformation of a given system into a statically determined primary system is essential for this method. The primary system is created by removing a certain number of joints of a given system and replacing them with appropriate reaction forces or moments. The displacement method is a method for solving statical systems where translational and rotational displacements of rigid joints are the unknowns. At the end, the method of initial parameters is presented and one example is solved in detail.