This paper reports the development of a general method for estimating the rates of lightning strikes on transmission lines using Monte Carlo simulation. Effects of towers, cross-arms, non-level ground, conductor sags and nearby structures are directly represented in the 3-dimension electrogeometric model (EGM). The method developed is a general one that is applicable to any transmission line configuration and is independent of the EGM used. Tedious analytical derivation of more than 100 equations for each configuration as required by analytical methods is avoided altogether. The formulation and a flow chart are detailed in the paper. The shortest distances from the lightning leader tip to individual structures that may be struck are evaluated and then compared with striking distances. The outcome of the comparison identities the structure which will be struck in each simulation. The exposure area adopted in the simulation is determined on the basis of the transmission line route length and the maximum possible striking distance to ensure that the simulation results in a maximum possible number of strikes on the overhead line. Strokes outside the exposure area will always miss the transmission line and, therefore, have no effects on the results. The method proposed and its software implementation are verified on the basis of results from analytical methods of earlier work, and from field data. (C) 1999 Elsevier Science S.A. All rights reserved.