Aims: A shape optimization technique is developed, using the boundary element method, for two-dimensional anisotropic structures to study the effects of anisotropy on the displacements and stresses, then minimize weight while satisfying certain constraints upon stresses and geometry. Study Design: Original Research Paper. Place and Duration of Study: Jamoum University College, Mathematics Department, between June 2016 and July 2017. Methodology: The shape design sensitivity analysis of a two-dimensional anisotropic structure using a singular formulation of the boundary element method is investigated to study the effects of anisotropy on the displacements and stresses. An Implicit differentiation technique of the discretized boundary integral equations is performed to produce terms that contain derivatives of the fundamental solutions employed in the analysis. This technique allows the coupling between optimization technique and numerical boundary ele...