A problem of allocating resources of a grid to workflow applications is considered. The problem consists, generally, in allocating distributed grid resources to tasks of a workflow in such a way that the resource demands of each task are satisfied. Grid resources are divided into computational resources and network resources. Computational tasks and transmission tasks of a workflow are distinguished. We present a model of the problem, and an algorithm for finding feasible resource allocations. A numerical example is included, showing the importance of the resource allocation phase on a grid. Some conclusions and directions for future research are given.