Water Distribution Networks (WDN) are systems of water distribution used in industrial processes and urban centers. The optimal WDN design can be very effective in saving energy, specifically in pumping service, to carry water to nodes of demand, at appropriated velocities and pressures. Indirectly, it can contribute in reducing liquid pollution and accidents caused by pressure overestimation in nodes. The design of WDN can be treated as an optimization problem with a Mixed Integer Nonlinear Programming (MINLP) formulation. The objective function, to be minimized is the WDN cost, given by the product of the pipe diameters and their lengths. The problem constraints are the mass balances in each node, the energy balances in the WDN loops and pressure and velocities limits. A set of commercial diameters is available, with proper costs and rugosity coefficients. The majority of paper published in this research field use external hydraulic simulators and meta-heuristic methods to solve the optimization problem. In the current paper a mathematical model using a deterministic Mathematical Programming approach is proposed and all variables are simultaneously optimized, avoiding the use of external software for pressure and velocities calculations. Two case studies were used to test the model applicability and coded in GAMS, using the global optimization solver BARON. Results showed that for both cases global optima was achieved, proving that it is possible to solve the problem, independently of external hydraulic simulator.