This chapter delves into the fundamental principles of stress analysis, essential for evaluating the integrity and performance of engineering structures under various loads. It starts by presenting the general stress state, comprising three normal stresses and six shearing stresses, and underscores the complexity involved in analyzing real-world structures compared to simple material tests. The focus then shifts to two-dimensional stress analysis, where plane stress conditions simplify the problem to two normal stresses and one shear stress. Key equations for determining the normal and shear stresses on inclined planes are derived, including methods for identifying the directions and magnitudes of principal stresses. The chapter also introduces Mohr’s circle, a graphical tool that provides a comprehensive understanding of stress transformations, principal stresses, and maximum shear stresses. Finally, illustrative examples demonstrate the practical application of these concepts in real-world scenarios, reinforcing the importance of accurate stress analysis in ensuring the safety and reliability of engineering designs.