Standardization of resource interfaces and behaviors is critical for realizing the Grid vision. Most works up to now mainly focus on technologies of accessing remote and heterogeneous resources. A twolayer framework for selecting and accessing resources on computational Grids is presented. It groups resources across organizations in an application oriented manner, and virtualizes each group of resources to be a set of stateful WEB services. These WEB services provide the capabilities for combining resources within, as well as across, organizations to prepare customized job execution environments as required. For every dynamically created execution environment, its lifecycle is allowed to span as long as desired to execute multiple jobs, and its interface and behaviors are standardized in an application oriented way. The framework has been implemented to virtualize resources in Harmonia, which is a software platform for coordinative computation and is utilized for developing the campus Grid of Peking University.