The p-median problem with maximum distance constraints between demand points and their respective nearest facilities is revisited. The authors present their computational experience on the use of Lagrangean relaxation and subgradient methods in the branch and bound procedure for solving this problem. The approach used in this paper is a direct approach in the sense that the maximum distance constraints are explicitly handled in the solution procedure. The authors’ computational experience shows that the method used in this paper is computationally viable, especially in a microcomputer-based environment. Comparative computational results are also reported.