The linear-elastic fracture mechanics (LEFM) is the main scope of this chapter. It covers the fundamentals of the LEFM and how they are applied to selecting the material, obtaining the stress level, and determining the crack sizes that prevent brittle fracture. Then, it is presented the Griffith model for developing fracture theory, the energy release rate, G, and the stress intensity factor, KI, and the critical stress intensity factor, KIc. It is also showed the correlation between G and K and the three basic crack opening modes. At the end it is introduced the fracture analysis procedures of the ASME Code Sections III and XI.