Normative reasoning is a type of reasoning that involves normative or deontic modality, such as obligation and permission. While large language models (LLMs) have demonstrated remarkable performance across various reasoning tasks, their ability to handle normative reasoning remains underexplored. In this paper, we systematically evaluate LLMs' reasoning capabilities in the normative domain from both logical and modal perspectives. Specifically, to assess how well LLMs reason with normative modals, we make a comparison between their reasoning with normative modals and their reasoning with epistemic modals, which share a common formal structure. To this end, we introduce a new dataset covering a wide range of formal patterns of reasoning in both normative and epistemic domains, while also incorporating non-formal cognitive factors that influence human reasoning. Our results indicate that, although LLMs generally adhere to valid reasoning patterns, they exhibit notable inconsistencies in specific types of normative reasoning and display cognitive biases similar to those observed in psychological studies of human reasoning. These findings highlight challenges in achieving logical consistency in LLMs' normative reasoning and provide insights for enhancing their reliability. All data and code are released publicly at https://github.com/kmineshima/NeuBAROCO.