Trust is one of the key factors that affect people's preferences in choosing cloud computing. However, the content and the evaluation basis of cloud trust are still not perfect, and there are lack of strict theoretical analysis and evaluation methods on its dynamic properties. For the status quo, this paper first defines cloud trust, and describes in details its sub-properties according to related international cloud security standards and trust specifications. Then, the basis, purpose, and scope of a model for analyzing cloud trust is presented. Next, to the process for building this model is described. Using LTS as an operational semantics profiling tool, starting from the interactive process of internal components in cloud, the cloud service is depicted as the interactions between users and cloud, and interactions among entities inside cloud. Finally, the model analysis tool, Kronos is used to analyze system state variations in service provision from multiple perspectives including availability, reliability and security. The analysis results demonstrate that the presented model can find not only known trusty problems but also unknown risks, which indicates the model is effective, and can provide theoretical support for trusted cloud construction.