General-purpose large language models (LLMs) excel in areas such as text generation but often struggle with formal reasoning. Therefore, specialized reasoning models such as o1 and DeepSeek-R1 have been developed, significantly improving performance in mathematical reasoning, programming, and logical inference. Nevertheless, natural language understanding often involves uncertain reasoning, such as modal reasoning and fuzzy reasoning. Current logical reasoning test sets primarily focus on first-order logic, propositional logic, and other fundamental forms of reasoning, but lack test sets for modal logic in natural language contexts. Therefore, we introduced the ModalLogicBench dataset to comprehensively evaluate the inference performance of both general-purpose and reasoning LLMs on 20 modal logic rules. These rules consist of the basic rules of five standard modal systems and the advanced rules obtained by integrating modal operators into propositional logic. We perform a detailed analysis of the modal inference capabilities of LLMs using zero-shot CoT. Experimental results show that reasoning LLMs demonstrate superior modal reasoning ability compared to general-purpose LLMs. Both reasoning and general-purpose LLMs perform well on most basic rules but struggle with some fundamental rules, such as possibility_closure in modal logic, and advanced rules, such as disjunctive_syllogism in modal form. It is worth noting that we observe process fallacies and failures in recognizing modal operators in the inference chains of models, which is particularly pronounced in general-purpose LLMs. Examples of task formats, generated prompts, and discussion cases are available at https://github.com/Limodal/AboutModalLogicBench .