ESDU 80036 introduces the concepts of linear elastic fracture mechanics and shows how these concepts may be used for analysing the behaviour of cracked structures under fatigue or static loadings. It describes the analytical method, based upon the stress intensity factor, and outlines the equations and limitations of usage. It shows how the stress intensity factor, K, which characterises the stress distribution in the vicinity of the crack tip, can be used to correlate crack propagation rate data and describes static failure (fracture toughness) and residual strength of materials under conditions where gross yielding does not occur. Details of how solutions for K may be obtained are discussed together with the effect of plasticity at the crack tip.