Although stitched laminates have been shown effective in preventing delamination failure, the presence of stitches results in a degraded in-plane strength and stiffness in such structures. The solution suggested in the paper is based on using stitches only in a part of the structure where they serve as arrestors of delamination cracks, while the part subject to considerable in-plane loading could remain unstitched. This approach, that could be called "functionally graded stitching," is considered on the example of a double cantilever beam (DCB) with a preexisting delamination crack that has penetrated into the stitched region of the beam. As is shown in the paper, the distribution of stitches in a functionally graded DCB (and in any other laminated structure) should be chosen to prevent three major failure modes. These modes include the failure of the stitches, bending failure of the unstitched delaminated section of the structure, and continuous crack propagation through the stitched region. The results obtained in the paper for the static problem clearly illustrate the feasibility of using functionally graded stitched laminates retaining in-plane strength and stiffness, while providing barriers to delamination cracks in less loaded regions of the structure. Additionally, the approach to the solution of the dynamic problem presented in the paper may be applied to the analysis of fatigue delamination cracks in partially stitched structures.