Large Language Models (LLMs) have become instrumental across various applications, with the customization of these models to specific scenarios becoming increasingly critical. System message, a fundamental component of LLMs, is consist of carefully crafted instructions that guide the behavior of model to meet intended goals. Despite the recognized potential of system messages to optimize AI-driven solutions, there is a notable absence of a comprehensive benchmark for evaluating how well LLMs follow system messages. To fill this gap, we introduce SysBench, a benchmark that systematically analyzes system message following ability in terms of three limitations of existing LLMs: constraint violation, instruction misjudgement and multi-turn instability. Specifically, we manually construct evaluation dataset based on six prevalent types of constraints, including 500 tailor-designed system messages and multi-turn user conversations covering various interaction relationships. Additionally, we develop a comprehensive evaluation protocol to measure model performance. Finally, we conduct extensive evaluation across various existing LLMs, measuring their ability to follow specified constraints given in system messages. The results highlight both the strengths and weaknesses of existing models, offering key insights and directions for future research.