The problem of allocating files in a computer network is a complex combinatorial problem due to the number of integer design parameters involved. These parameters include system cost, number of copies of each file to be stored, and sites at which the copies should be stored. The tradeoffs between these parameters are discussed. The design problem is formulated as an integer programming problem. A branch and bound algorithm is proposed to solve the problem. A linear programming formulation which ignores integer restrictions (and allows a fraction of a file to reside at a site) is shown to yield integer solutions in most cases. In other words integer restrictions are satisfied automatically. A near-optimal heuristic is presented, along with computational results. An efficient method to solve the file allocation problem for medium-scale networks is proposed.