Abstract: High-rise buildings not only increase urban land use efficiency, but also facilitate the attainment of conditions required for lightning leader initiation due to enhanced electric field distortion at the top, thereby increase lightning activity occurrence. To address the complexity of lightning strike process of high buildings, a 3-dimensional stochastic physical model of lightning strike to high-rise buildings is developed, based on a conventional physical model of lightning strike and considering downward negative ground flashes. The influence of building geometry on upward leader initiation and attachment process is numerically simulated. Five different geometric shapes (long lightning rod tower-shaped, cuboid-shaped, cuboid-tower-shaped, cylindrical-tower-shaped, slope-shaped) and different heights (100-500 m) of buildings are designed, and their effects on the initiation time of upward leader, the length and rate of upward leader and the striking distance are comparatively analyzed. The shape and height of a building have significant impacts on the initiation and attachment process of the upward leader. It is concluded that in the order of long lightning rod tower-shaped, cylindrical-tower-shaped, cuboid-tower-shaped, slope-shaped and cuboid-shaped buildings, the initiation time of a stable upward leader becomes progressively later, while the length of the upward leader and the striking distance are progressively reduced. Under the same conditions, the average initiation time of the stable upward leader of the cylindrical tower is about 0.26 ms earlier than that of the cuboid tower, the average length of the upward leader is increased by about 60 m, and the average striking distance is increased by about 30 m. A taller building height corresponds to an earlier initiation of the stable upward leader. For every 100-m increase in the height of a cuboid-tower structure, the electric field intensity at its tip is about doubled. Compared to a 100-m tall cuboid, the average upward leader length of a 500-m cuboid is extended by about 60 m, and the average striking distance increases by roughly 36 m. Tall buildings with sharp shapes at the top are not only easier to trigger the upward leader, but also promote faster leader development and increase the likelihood of attachment to a downward leader.