AbstractSoft network materials with biomimetic mechanical properties such as a negative Poisson’s ratio have important applications in tissue engineering, biomedical devices, and soft robotics. Several finite-element (FE)-based design strategies have been developed to produce network materials with prescribed mechanical properties. However, obtaining network designs with a prescribed negative Poisson’s ratio over large strain remains a challenge. Here, an optimization framework was developed using isogeometric analysis and a genetic algorithm for the design of soft missing rib structures with controllable negative Poisson’s ratios over large strains. The missing rib structures with six ligaments were optimized to achieve constant negative Poisson’s ratios ranging from −0.1 to −0.6 up to 70% tensile strain under plane stress condition. The optimization framework was employed to obtain a missing rib network design with deformation behavior closely matching that of cat’s skin up to 90% tensile strain. This optimized design was fabricated using a biocompatible material via liquid additive manufacturing and validated experimentally, demonstrating the potential of the soft missing rib designs for biomedical applications.