Mechanical metamaterials enable customizing the elastic properties of physical objects by altering their fine-scale structure. Numerous recent works in graphics, mechanical engineering and computational fabrication have focused on the design of metamaterials with controlled physical properties by optimizing the shape of microstructures. However, our work is the first to comprehensively analyze and design the finite-deformation behaviors of 2D microstructures, which has required several novel computational techniques. We can substantially improve the material property fit for a wide range of properties, achieving a highly linear response. Our optimization simultaneously eliminates the collisions and improves the material property fit.