Abstract This paper presents and analyses a possible extension of the well-known mean Strain Energy Density approach, proposed and developed by Paolo Lazzarin for the strength characterization and for the structural analysis of sharp notches. The new parameter, that here will be defined and discussed only for the case of a crack subjected to mode I loading conditions, will be shown to be able to characterize the superficial energy per unity of area due to the presence of a crack in a plate. Then it can be considered to be an Intensity Factor, in analogy to the Stress Intensity Factor KI. For this reason it will be called the Strain Energy Density Intensity Factor (SEDIF). Aim of the introduction of this new approach is to simplify both the characterization of the material and the structural analysis of the components, since the proposed parameter does not depend on the strength of an un-notched specimen taken as reference and does not need the evaluation of the radius R0 of the area to be considered for the evaluation of SED. Two in some way similar parameters (the J integral and the S factor proposed by Sih) will be discussed and compared to the proposed Strain Energy Density Intensity Factor.