In India, the natural energy resources (thermal and hydro) are unevenly distributed and are mostly present in the remote areas and the load centers are distributed across various regions of the country. Therefore high voltage lines have become necessary for the devel-opment of large interconnected power networks and for the reliable and economic transfer of power. The increase in electric power demand due to the electric load growth has lead to the expansion of the transmission systems to ultra high voltage levels. Presently, Ultra High Voltage (UHV) power transmission lines are being built to transfer large electric power to distant load centers from the generating stations. Increasing the line voltage increases the surge impedance loading, stability and the thermal capacity of the line. Lightning is one of the major causes for the line outages and interruptions of UHV power lines. A lightning strike generates a very large voltage leading to insulator puncture, melting, burning and pitting of conductors and the supporting hardware. Lightning can lead to transient over-voltages thus leading to ash-over in the power transmission lines which are dangerous for the power equipments as well as for the human beings working in the vicinity. Ground wires are used for the protection of overhead power transmission lines against a lightning stroke. The overhead ground wires are installed such that the lightning attaches to it and shunts the lightning current to the ground through the tower, thus protecting the phase conductors. Shielding failure happens when the lightning strikes the phase conductor instead of the ground wires. Lightning shielding failure is a major con-cern in UHV lines due to their large height, very high operating voltage and wide exposure area of the phase conductors. The lightning over-voltages injected on the phase conductor (shielding failure) nally reaches the substation causing serious threat to the substation components and can lead to temporary or permanent outage of the power transmission system. There have been cases of very high shielding failure ash-overs of UHV lines and thus lightning attachment to power transmission lines need to be studied in detail to reduce the power system line outages. Several models such as electro-geometric model (EGM) and leader progression model (LPM) have been developed to study the shielding failure of power transmission lines. EGM has been extensively used to obtain lightning attachment to power transmission lines but in recent years it is seen that EGM is unable to accurately predict the lightning attach-ment to UHVAC lines. The shielding failure rates obtained by EGM does not match with the observed shielding failure rate for UHV lines. For this reason LPM is considered to obtain lightning attachment to UHV lines but LPM in its initial stage do not deal with the detailed physics of the upward leader inception, i.e., corona inception and unstable as well as stable upward leader inception from the object on the ground. In this thesis a model for the lightning attachment has been developed based on the present knowledge of the lightning physics. The thesis mainly focuses on the modelling of upward leader inception and propagation for lightning attachment to UHV power trans-mission lines. Upward leader inception is modeled based on the corona charge present near the conductor region and the upward leader propagation model is based on the correlation between the lightning induced voltage on the conductor and the voltage drop along the upward leader channel. The present model considers corona inception and modelling of unstable and stable upward leader inception from the ground object for the analysis of the lightning attachment process. The upward leader inception model developed is compared with the previous inception models and the results obtained using the present and previous models are found to be comparable. Lightning striking distances ( nal jump) for various lightning return stroke current were computed for di erent conductor heights using present lightning attachment model. It is seen that the striking distance increases with the increase in lightning re-turn stroke current and increases with increase in conductor heights. The striking distance computed using the present model matches with the value calculated using the equation proposed by the IEEE working group for the applicable conductor heights of up to 8 m. The in uence of the conductor operating voltage, cloud electric eld, lightning down-ward leader lateral distance, conductor length, transmission line tower and conductor sag on the upward lightning leader inception are analysed and reported in the thesis. It is found that the lightning attraction to power transmission line increases with increase in conductor positive operating voltage and decreases with increase in conductor negative op-erating voltage. The presence of transmission line tower reduces the lightning attachment to the conductor lines and the probability of lightning strike decreases with the increase in downward leader lateral distance from the conductor lines. The present lightning attachment model is applied to study the shielding failure of UHV power transmission lines rated for 1200 kV ac (delta and horizontal con guration) and for 800 kV dc (with and without a dedicated metallic return conductor) and thereby the lightning shielding failure ash-over rate is computed for the UHV power transmission lines. It is seen that the lightning shielding rate for UHV power transmission lines depend on the lateral distance of the downward leader channel, instantaneous 50 Hz voltage on the transmission line conductor, height of the transmission line conductor, induced voltages on the conductor and the lightning return stroke current.