A Computational Grid is a collection of heterogeneous computers and resources spread across multiple administrative domains with the intent of providing users easy access to these resources. There are many ways to access the resources of a Computational Grid, each with unique security requirements and implications for both the resource user and the resource provider. A comprehensive set of Grid usage scenarios is presented and analyzed with regard to security requirements such as authentication, authorization, integrity, and confidentiality. The main value of these scenarios and the associated security discussions is to provide a library of situations against which an application designer can match, thereby facilitating security-aware application use and development from the initial stages of the application design and invocation. A broader goal of these scenarios is to increase the awareness of security issues in Grid Computing. A computational grid is a hardware and software infrastructure that provides dependable, consistent, pervasive, and inexpensive access to high-end computational capabilities.