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The stress state surrounding wounds in the skin plays an important role in the healing process; it affects the tissue strength, its aesthetic, and its resistance to infections. In this paper, the collagen fibril and elastin matrix damage mechanics following suture point application is investigated at the nanoscale; to this purpose, a model has been developed, which accounts for the architectural and mechanical features of the tissue components. Results indicate that the force displacement caused by the suture point application curve initially stiffens and subsequently softens. Softening occurs due at first to the enlargement of the elastin matrix damaged area and second to the collagen fibril disruption. Three regions may be identified: the first one, (0-0.38 N) refers to skin withstanding the force both in the collagen and elastin components; the second one (0.38-0.75 N) concerns the mechanism of elastin matrix damage; in the last one (>0.75 N), the collagen fibrils also fail. Accordingly, by properly choosing the number of suture points, it is possible to define the optimal suture points number for a given wound closure force.