Transients caused by lightning that strikes to transmission lines, switching operations or faults, are fundamentals in selecting equipment insulation levels and protection devices. Thus, studies of electromagnetic transients on transmission lines have demonstrated that when a change on the normal operation of the system takes place, voltage and currents traveling waves appear and these are reflected and refracted in the transmission line. In this paper, an ATPDraw simulator is developed to observe the propagation of voltage and current traveling waves along the transmission lines. The Bewley's Lattice diagram is used into the simulator to show in a comprehensive manner the behavior of the traveling waves. The behavior of the traveling waves is strictly depending on the reflection and refraction coefficients in the sending and receiving nodes, in turn these coefficients are depending on the transmission network's parameters, such as the characteristic impedance and the impedance of the sending and receiving ends.