This paper describes the model and software tools for virtualization of the Grid execution environment. The basic assumption of this study is that Virtual Grid (VG) is constructed dynamically according to application requirements with virtualized computational and communication resources. A VG instance is dynamically created for each application and its initial configuration can be further modified during runtime to satisfy the requested level of resource usage and to maintain the quality of service indexes at agreed-upon values. A VG model that takes into account this approach has been proposed and analyzed in the context of Grid-related technology.