A systematic Laplace method is presented for the determination of transient-current propagation in a single transmission line. Earth distortion and skin effects are considered in the analysis. The method permits a quick and accurate evaluation of these currents without using numerical-integration techniques. From the theoretical study, an efficient method of digital simulation is also derived for a simpler current evaluation in computers. Both analytical and simulation expressions are in terms of line and earth parameters, which enables an easy computation of transient current propagation in different transmission lines to be carried out. Results are in good agreement with those obtained by other investigations. Part 1 of the paper deals with a basic single line which would represent either an a.c. or a d.c. scheme. Part 2 of the paper deals with polyphase systems with lossy earth returns (see p. 137).