The method presented permits the analysis of solid samples by atomic absorption spectroscopy without any preparation. For this purpose microgram amounts of the substance to be analyzed are vaporized effectively by focusing the radiation of a neodymium pulse laser on the sample. The absorption by free and neutral atoms of the vapour cloud is measured photoelectrically. By means of an acousto-optical Q-switch the laser generates a train of spikes with constant time intervals, in contrast to other types of Q-switches. This results in the removal of sample material over the total duration of the laser pulse. In Part I we have investigated how the experimental conditions of the Q-switched laser influence the mass of the substance evaporated by each pulse, the expansion of the plume as well as its emission and absorption. By space and time resolved measurements experimental parameters have been examined which pertain to the observation of atomic absorption. The method described combines the advantages of atomic absorption spectroscopy (simple instrumentation, selectivity, and power of detection) with those of laser methods; it is particularly useful, if only a limited amount of a solid sample is available or, as with inclusions, this has to be vaporized directly. In this case it is possible to get a quantitative analysis of a single element with only a small number of laser shots. Detailed examples of analytical applications as well as the capability of this method (sensitivity, limits of detection, and accuracy) will be presented in Part II of this paper.