In order to investigate the influences of mountainous terrain on lightning induced voltages

a two-dimensional finite-difference time-domain（2-D FDTD） method was proposed to calculate the lightning induced voltages of overhead lines in hilly terrain. The validation of the FDTD algorithm was verified by comparing with the relevant research results abroad. The effects of the inclination angle

conductivity as well as its stratified structure on the lightning induced voltages of overhead lines were also calculated by the method proposed in this paper. The results show that

compared with the ideal flat terrain

the slope of the mountain terrain has a significant impact on the lightning overvoltage

especially in the case of limited soil conductivity

and the overvoltage amplitude increases significatly with the increase of the terrain slope; when the conductivity of surface soil is lower than the conductivity of lower-layer soil（σ1<σ2）

the induced overvoltage amplitude increases significantly as the thickness of surface soil increases; while the conductivity of surface soil is larger（σ1>σ2）

the lightning overvoltage amplitude decreases rapidly as the thickness of surface soil increases. When the thickness of surface soil exceeds 5 m

the overvoltage amplitude mainly depends on the conductivity of surface soil

and the influence of soil stratification can be neglected. The research results can provide a theoretical reference for lightning protection design of mountainous overhead transmission and distribution lines.