In view of the lack of information on shape optimization in composite media, it was decided to do a pilot study involving a hole in a laminated plate subject to in-plane biaxial tension. Classical plate lamination theory is used, together with a finite element approach. Minimizing the maximum values of certain failure functions \(\Phi\) is taken to be the objective. In the single-ply case it can be shown that the optimality condition is that the mutual strain energy is constant on the design boundary under the condition that the design boundary has no geometrical constraint [see the second author, K. T. Chung, T. Torigaki and J. E. Taylor, ibid. 57, 67-89 (1986; Zbl 0578.73081); eq. 10; 20]. For isotropic media, it has also been shown that the optimality condition is \(\Phi=\)constant on the hole boundary. This, so far, has not been proven for anisotropic media. Here, analogous to the isotropic case, it is postulated that the maximum value of \(\Phi\) occurs on the hole boundary. At all stages of the numerical work this was monitored numerically and found to be true. Moreover \(\Phi=\)constant on the hole boundary is postulated as the optimality condition. This, in general, will not lead to a global optimum (in view of the possibility of multiple holes), but it should lead to a local minimum. Of particular interest was to see whether the techniques developed for shape optimization in isotropic media would work for laminated composites, involving as they do much larger stress gradients.