The stress concentrations are of many types and of different levels. For brittle and quasi-brittle materials, failure criteria proposed by different authors are established to study different situations. For example, when a stress distribution is not uniform but does not present a singularity, the maximum stress criterion (σ = σ
) is used. For the case of a crack, the criteria are based on the Linear Fracture Mechanics. When a stress concentration presents a singularity but weaker than a crack one, such as sharp notches, the failure criteria are kinds of combination of the criteria for the two above cases. In fact, each criterion only functions with a particular stress concentration case for which it was developed. Its extension to a more general case often induces important errors. Therefore, the purpose of the present work is to establish a unified crack onset criterion for brittle and quasi-brittle materials that enables to count for all types of stress concentrations.