Transmission towers play a vital role in power distribution networks and are often subject to strong wind loads. Lattice tower design is often based on a linear elastic response to wind loading using methodology derived for atmospheric boundary layer (ABL) winds. A number of failures have been attributed to high intensity wind (HIW) events such as downbursts and tornadoes. This thesis investigates extreme winds on a self-supported lattice transmission tower and ultimately makes comparisons of the capacity under ABL and HIW. The force-deformation relation between the base shear and the displacement of the tip of the tower are used to represent the capacity curve of a structure under wind loading. Wind tunnel testing is used to evaluate the aerodynamic behaviour of a typical tower cross-arm section, which serves as the basis for selection of wind loading expressions for the numerical model. Recommendations are made for further investigation of lattice aerodynamics, including a more robust definition of the drag coefficient. Capacity estimates obtained using the incremental dynamic analysis (IDA) and nonlinear static pushover (NSP) procedures are compared, which indicate good agreement for ABL winds. The analyses consider both geometric and material nonlinearity. The NSP analysis is used to estimate the capacity of the tower under various wind profiles for the transverse and longitudinal wind directions, and it is shown that the capacity curve obtained under typical downburst scenarios can be approximately enveloped by those obtained under rectangular and ABL wind profiles. An uncertainty propagation analysis is carried out using the simple Monte Carlo technique, which shows that the coefficient of variation of the tower capacity is small compared to that associated with extreme wind load effects. Oblique wind directions are considered for ABL, rectangular and downburst wind loading, which associate critical wind speeds with direction. The resulting capacity curves are used to develop the capacity surface of the tower. It is shown that a conservative approximation of the tower capacity curve, or surface, under downburst wind is made if a fully correlated ABL wind loading profile is used as the wind load distribution.