The recent emergence of cloud computing has drastically altered everyone's perception of infrastructure architectures, software delivery, and development models. Projecting as an evolutionary step, cloud computing encompasses elements from grid computing, utility computing, and autonomic computing into an innovative deployment architecture. Cloud computing systems offer a lot of advantages like pay per use and rapid service provisioned on demand, while it suffers for some concerns specially security. In fact, a number of unchartered risks and challenges have been introduced from this new environment. This chapter explores the security issues in cloud computing systems and shows how to solve these problems using a quantitative security risk assessment model.