Carbon fiber reinforced plastic (CFRP) structures are highly sensitive to delaminations, resulting from low energy impacts or manufacturing defects. Non-linear numerical algorithms are mandatory to investigate the complex mechanisms governing the delamination growth phenomena. Although the high computational costs associated to the non-linear algorithms are acceptable in a detail verification design stage, less expensive procedures are desired in a preliminary design stage or during optimization procedure. In this work, a fast numerical procedure, able to determine the delamination growth initiation in composite structures in the framework of a damage tolerant design approach when mixed mode I and II growth is expected, is introduced. The state of the art of the fast delamination growth procedures is critically discussed and improvements to the existing approaches are proposed to extend their applicability and to increase their accuracy. Comparisons with the standard non-linear delamination growth approaches are presented to assess the effectiveness of the proposed novel Fast approach. The results of the proposed fast approach are comparable with the ones obtained by means of standard numerical non-linear technique, allowing up to 95% computational cost saving.