This paper introduces an automated design framework for discovering flexible mechanical metamaterials with specific nonlinear dynamic responses. The framework leverages a fully differentiable simulation environment and gradient-based optimization to tailor the material's behavior for tasks such as energy focusing, energy splitting, dynamic protection, and nonlinear motion conversion. The design strategy involves four steps: deriving the equations of motion, defining the design space, performing optimization, and fabricating and testing the designs. The authors demonstrate the effectiveness of their approach by designing metamaterials that can switch between different tasks, such as focusing energy at two distinct locations using static pre-compression. The results show that the optimized designs exhibit robust performance and can be physically realized and tested, highlighting the potential of the framework in creating reprogrammable nonlinear dynamic metamaterials.This paper introduces an automated design framework for discovering flexible mechanical metamaterials with specific nonlinear dynamic responses. The framework leverages a fully differentiable simulation environment and gradient-based optimization to tailor the material's behavior for tasks such as energy focusing, energy splitting, dynamic protection, and nonlinear motion conversion. The design strategy involves four steps: deriving the equations of motion, defining the design space, performing optimization, and fabricating and testing the designs. The authors demonstrate the effectiveness of their approach by designing metamaterials that can switch between different tasks, such as focusing energy at two distinct locations using static pre-compression. The results show that the optimized designs exhibit robust performance and can be physically realized and tested, highlighting the potential of the framework in creating reprogrammable nonlinear dynamic metamaterials.