The paper deals with a transient analysis of a straight thin wire in a presence of a two-media configuration using a simplified reflection coefficient approach. A direct time domain formulation is based on thin wire antenna theory and on the corresponding space–time integral equation for the wire above a dissipative half-space, or buried in a real ground. The effect of a half-space is taken into account via the simplified reflection/transmission coefficient arising from the modified image theory. The resulting space–time integral equation for the wire above and below ground, respectively, is handled via the time domain Galerkin–Bubnov variant of the indirect boundary element method (GB-IBEM) and some illustrative numerical results are presented. The transient response computed via the simplified reflection/transmission coefficient approach is compared, where possible, to the results obtained via the Fresnel coefficients approach.