There has been significant effort to build high throughput computing systems out of many distributed multimedia servers. These systems should accommodate a larger number of servers and should handle the ever-growing user demands. Recently, Grid computing has become one of the promising technologies that can deliver such a system. Among the many problems encountered in building Grid computing systems, resource discovery, overhead reduction, workload balancing and fault tolerance are the most challenging. In this paper, we present a resource discovery and allocation mechanism (RDAM) in a computational Grid system.