This paper studies the problem of dynamical system modeling, which involves the evolution of multiple interacting objects. Recent data-driven methods often utilize graph neural networks (GNNs) to learn these interactions by optimizing the neural network in an end-to-end fashion. While large language models (LLMs) have shown exceptional zero-shot performance across various applications, their potential for modeling dynamical systems has not been extensively explored. In this work, we design prompting techniques for dynamical system modeling and systematically evaluate the capabilities of LLMs on two tasks, including dynamic forecasting and relational reasoning. An extensive benchmark LLM4DS across nine datasets is built for performance comparison. Our extensive experiments yield several key findings: (1) LLMs demonstrate competitive performance without training compared to state-of-the-art methods in dynamical system modeling. (2) LLMs effectively infer complex interactions among objects to capture system evolution. (3) Prompt engineering plays a crucial role in enabling LLMs to accurately understand and predict the evolution of systems.