This paper offers a comprehensive survey of numerical methods for duct and pipe network optimization.- Only tree networks are considered. Procedures reviewed, analyzed, and compared include Coordinate Descent. Penalty Function. Lagrange Multipliers, Reduced Gradient, and Dynamic Programming. In all cases the objective function is the present worth of the total life-cycle cost. Constraints, such as standard pipe or nominal duct diameters, maximum velocities, pressure balancing, and other nonlinear or integer functions are applied to the problem. Recommendations for microcomputer programs to optimize pipe and duct networks are given.