This paper deals with the problem of assigning tasks to the processors of a multiprocessor system such that the sum of execution and communication costs is minimized. If the number of processors is two, this problem can be solved efficiently using the network flow approach pioneered by Stone. This problem is, however, known to be NP-complete in the general case, and thus intractable for systems with a large number of processors. In this paper, we propose a network flow approach for the task assignment problem in homogeneous hypercube networks, i.e., hypercube networks with functionally identical processors. The task assignment problem for an n-dimensional homogeneous hypercube network of N (=2n) processors and M tasks is first transformed into n two-terminal network flow problems, and then solved in time no worse than O(M3 log N) by applying the Goldberg-Tarjan's maximum flow algorithm on each two-terminal network flow problem.