Large Language Models (LLMs) are widely used in natural language processing but face the risk of jailbreak attacks that maliciously induce them to generate harmful content. Existing jailbreak attacks, including character-level and context-level attacks, mainly focus on the prompt of the plain text without specifically exploring the significant influence of its structure. In this paper, we focus on studying how prompt structure contributes to the jailbreak attack. We introduce a novel structure-level attack method based on tail structures that are rarely used during LLM training, which we refer to as Uncommon Text-Encoded Structure (UTES). We extensively study 12 UTESs templates and 6 obfuscation methods to build an effective automated jailbreak tool named StructuralSleight that contains three escalating attack strategies: Structural Attack, Structural and Character/Context Obfuscation Attack, and Fully Obfuscated Structural Attack. Extensive experiments on existing LLMs show that StructuralSleight significantly outperforms baseline methods. In particular, the attack success rate reaches 94.62\% on GPT-4o, which has not been addressed by state-of-the-art techniques.