The paper deals with a transient analysis of a straight thin wire in a two media configuration using a simplified reflection coefficient approach. The formulation is based on the corresponding Hallen integral equation. The effect of a half-space is taken into account via the simplified reflection coefficient arising from the modified image theory. The Hallen equation is solved via the Galerkin Bubnov variant of the indirect Boundary Element Method (GB-IBEM) and some illustrative numerical results are presented.