Use case modeling employs user-centered scenarios to outline system requirements. These help to achieve consensus among relevant stakeholders. Because the manual creation of use case models is demanding and time-consuming, it is often skipped in practice. This study explores the potential of Large Language Models (LLMs) to assist in this tedious process. The proposed method integrates an open-weight LLM to systematically extract actors and use cases from software requirements with advanced prompt engineering techniques. The method is evaluated using an exploratory study conducted with five professional software engineers, which compares traditional manual modeling to the proposed LLM-based approach. The results show a substantial acceleration, reducing the modeling time by 60\%. At the same time, the model quality remains on par. Besides improving the modeling efficiency, the participants indicated that the method provided valuable guidance in the process.