This report provides a detailed investigation into buffer overflow vulnerabilities, a critical security concern in software development. It begins with an introduction to vulnerability investigation and the significance of detecting and mitigating software weaknesses. The main body of the report focuses on buffer overflow vulnerabilities (CVE-2021-3156 and CWE-121), explaining their nature, merits, demerits, consequences, affected environments, and severity. It then delves into the underlying flaws, how these vulnerabilities work, and methods for attack detection. The report highlights combinatorial testing as a detection methodology, discussing its advantages and disadvantages, along with the use of specific testing tools. Finally, it explores preventive measures and mitigation strategies, and concludes with a critical reflection on the work undertaken and the personal development achieved.