In this paper, fundamentals of the transmission-line-modeling or matrix (TLM) method are briefly explained. Then, it is applied to analyzing transient electromagnetic fields produced by a current wave propagating along a simulated vertical lightning return-stroke channel, and surges on a simple conductor system. In both applications, the TLM-calculated field and surge waveforms agree well with the corresponding waveforms calculated theoretically and/or using the finite-difference time-domain method.