Sticky ends are unpaired nucleotides at the ends of DNA molecules that can associate to link DNA segments. Self-assembly of DNA molecules via sticky ends is currently used to grow DNA structures with desired architectures. The sticky end links are the weakest parts of such structures. In this work, the strength of sticky end links is studied by computational means. The number of basepairs in the sticky end and the sequence are varied, and the response to tension along the axis of the molecule is evaluated using a full atomistic model. It is observed that, generally, increasing the number of basepairs in the sticky end increases the strength, but the central factor controlling this parameter is the basepair sequence. The sticky ends are divided into two classes of low and high strength. The second class has strength comparable with that of a double stranded molecule with one nick in one of the strands. The strength of the first class is roughly half that of the strong sticky ends. For all strong sticky ends tested, the enhanced stability is associated with the formation of an unusually stable complex composed from two basepairs and two flanking bases of certain sequence. This complex rotates and aligns with the direction of the force allowing significant deformation and providing enhanced strength. This is similar to a mechanism recently suggested to enhance the mechanical stability of an RNA kissing loop from the Moloney murine leukemia virus. The model is tested against experimental structural data for sticky ends and against published simulation results for the stretch of double stranded DNA. The results provide guidance for the design of DNA self-assembled structures and indicate the types of sticky ends desirable if maximizing the strength and stability of these structures is targeted.