•Suture shapes were automatically generated using a line descriptor method.•Analytical and finite element models were developed to determine the pullout response and maximum tensile stress in the suture materials.•The material response can be tuned with geometrical parameters like interlocking angle θ0, plateau length d/R0, and radii ratio R0/R1.•Coefficient of friction between suture interfaces also plays an important role in the material response.•A ``brute force'' optimization scheme showed that to optimize the maximum strength and energy absorption, it is preferable to use lo friction coefficient for all types of sutures. Hard structural elements in nature are often joined with sutures lines, as seen in human skull, cephalopods or turtle shell. These sutures can arrest cracks, and can provide flexibility for respiration, locomotion or growth. In this paper we introduce a morphometric method to capture the complex shape of sutured interfaces using only a few parameters. The method is simple, and can capture relatively complex suture geometries with re-entrants, interlocking features. The study starts with a simple jigsaw-like model which is enriched with additional features (plateau regions in dovetail-like sutures, multiple locking sites). For each case, closed form and finite elements solutions are developed to capture the full nonlinear pullout response and to predict the maximum stress (and potential fracture) in the solid material. These models were then used to identify the geometries and interface properties (friction) that lead to optimum combinations of strength and energy absorption. Suture designs that reduced frictional stress with low coefficient of friction or with multiple contact points were the most efficient. The results can serve as guidelines to design and optimization of non-adhesive sutures with arbitrary shapes made of arc of circles and lines. We found that the best designs involve low coefficient of friction, which raises an interesting hypothesis on the function of the protein layer in natural sutured lines: This soft layer could act as “lubricant” to prevent the fracture of the solid structures.