This dissertation is devoted to the study and analysis of lightning overvoltages in overhead transmission lines using the software package EMTP (Electromagnetic Transients Program). The lightning phenomenon was analysed in detail and an electric model was established using a controlled current source. The waveshapes associated to the lightning current were also characterized. The most relevant electrical power system devices were modelled to accommodate the transient effects related to the lightning phenomenon. To achieve this goal, some dynamic link libraries (dll) were developed and/or modified in order to consider new models in the commercial software EMTP. Considering different current waveshapes as well as different models for the towers, for the grounding electrodes and for the insulation flashover, several simulations were performed and the voltages in the phase conductors, in the earth wires and in the insulators were evaluated. Sensitivity analysis was also performed considering the most relevant parameters. Demonstrative studies were also performed to show the application of different models and some important conclusions, that can be used successfully to design the overhead transmission lines and the protective schemes as well as to specify the insulation coordination requirements, were extracted.