This chapter summarizes the principles of the displacement-based finite element method (FEM) for stress and strain analysis. An analysis of the FEM can be generally outlined into the following six steps: discretization of a system; determination of a displacement model; Analysis of mechanical properties of an element; calculation of equivalent nodal forces, assembly of element stiffness equations and establishment of the equilibrium equations for an entire system; and solution of unknown nodal displacements; and calculation of element stresses. Before discussing the problems of continuum media, the chapter presents a simple structure with two articulated rods. This example is presented to understand the concept about how to determine mechanical properties of individual elements and how to obtain the force-displacement relation for the entire structure. Since the rods are linked through hinges at which frictional moments can be neglected, the force and displacement at each node only have two components, i.e., two degrees of freedom.