The optimum economic sizing of a water distribution network has been focus of study for many researches and projectors, and represent a relevant part of sanitation programs. But, by now, the known works approaches only the implantation cost, considering that the pipes have biggest heavy in the project. So, the problem is reduced to sizing pipes which objective is reach a cheaper network and satisfying the minimum hydraulic prerequisites. This leads to the choice of a network with pipes of minor diameters since this choice satisfies the hydraulics restrictions. New in Brazil by now, our approach consider too the maintenance cost throughout life span of network. It because, if in one way the larger diameters are more expensive, in an other, it are more resistant to break and to rugosity effects. This leads to a network of minimum maintenance cost throughout its life span. Then, we reach the equilibrium between the implantation cost and the maintenance cost.