In this chapter, the stiffness matrix of a two-node bar element is derived. The bar is a structural element with axial and torsional stiffness, but only the axial stiffness is considered in this derivation. The methodology behind this derivation is presented in Sect. 2.1. Section 2.2 details the assumptions underlying the finite element bar definition and specifies the associated geometric data. The derivation of the stiffness matrix employs the Principle of Virtual Displacements (PVD), a concept grounded in classical mechanics and variational calculus. PVD serves as a core tool for formulating equations of motion in mechanical systems. A virtual displacement is an infinitesimal, hypothetical displacement consistent with the system’s constraints. According to PVD, the total virtual work of both external and internal forces equals zero for any such permissible virtual displacement when a system is in equilibrium. Three distinct approaches are used throughout this chapter to evaluate the stiffness matrix: