Cloud computing technology is a relatively new concept of providing scalable and virtualized resources, software and hardware on demand to consumers. It presents a new technology to deliver computing resources as a service. It offers a variety of benefits like services on demand and provisioning and suffers from several weaknesses. In fact security presents a major obstacle in cloud computing adoption. In this chapter, we will deal with security problems in cloud computing systems and show how to solve these problems using a quantitative security risk assessment model named Multi-dimensional Mean Failure Cost (M2FC). In fact, we present first a deep analysis of security issues related to cloud computing environments and then propose a generic framework that analysis and evaluate cloud security problems and then propose appropriate countermeasures to solve these problems.