Small language models (SLMs) have emerged as promising alternatives to large language models (LLMs) due to their low computational demands, enhanced privacy guarantees and comparable performance in specific domains through light-weight fine-tuning. Deploying SLMs on edge devices, such as smartphones and smart vehicles, has become a growing trend. However, the security implications of SLMs have received less attention than LLMs, particularly regarding jailbreak attacks, which is recognized as one of the top threats of LLMs by the OWASP. In this paper, we conduct the first large-scale empirical study of SLMs' vulnerabilities to jailbreak attacks. Through systematically evaluation on 63 SLMs from 15 mainstream SLM families against 8 state-of-the-art jailbreak methods, we demonstrate that 47.6% of evaluated SLMs show high susceptibility to jailbreak attacks (ASR > 40%) and 38.1% of them can not even resist direct harmful query (ASR > 50%). We further analyze the reasons behind the vulnerabilities and identify four key factors: model size, model architecture, training datasets and training techniques. Moreover, we assess the effectiveness of three prompt-level defense methods and find that none of them achieve perfect performance, with detection accuracy varying across different SLMs and attack methods. Notably, we point out that the inherent security awareness play a critical role in SLM security, and models with strong security awareness could timely terminate unsafe response with little reminder. Building upon the findings, we highlight the urgent need for security-by-design approaches in SLM development and provide valuable insights for building more trustworthy SLM ecosystem.