This paper presents a mathematical model and a methodology to solve the transmission network expansion planning problem considering uncertainness in demand. The methodology allows us to find an optimal transmission network expansion plan that allows the power system operates adequately in an environment with uncertainness. The model presented is solved using a genetic algorithm designed to solve the expansion planning with uncertainness in demand in an efficient way. The results obtained for several known systems from the literature show the excellent performance of the proposed methodology. © 2005 IEEE.