The failure of transmission line structures due to severe High Intensity Wind (HIW) events is one of the major problems facing the electrical utility companies in various places around the globe including Canada. An extensive research program focusing on this problem started about fifteen years ago at The University of Western Ontario (UWO). In this Thesis, two major milestones are achieved leading to the advancement of the knowledge in this field. The first milestone is conducting, for the first time, a test on an aero-elastic model of a multi-span transmission system under reduced–scale simulated downbursts. The first objective of the experimental program is to assess the dynamic response of the conductors and the towers resulting from the transient nature of both the mean and the fluctuating components of downbursts. The second objective is to use the experimental results to validate a numerical model previously developed in-house at UWO for the analysis of transmission line structures under downbursts. The second milestone achieved in this Thesis is the development, for the first time, of a set of load cases that simulates the critical effects of downbursts on transmission line structures taking into account the variation in the location and size of the wind events. A load case that is particular for downbursts results in a velocity profile on the line that is non uniform and unequal along the conductor spans adjacent to the opposite sides of a tower. This leads to unequal tensions in the two spans adjacent to the tower and the difference in tensions leads to a force transmitted to the tower along the longitudinal direction of the line. This force is believed to be the cause of the failure of many towers. A procedure that is simple enough for application and for estimation such a force is developed in this study. Finally, through conducting an extensive parametric study for a number of transmission line systems, a comprehensive and simple procedure for estimating critical downburst loads on both the tower and the conductors is developed and presented in a simplified manner for possible implementation in the codes of practice