We discuss the use of a genetic algorithm (GA) to invert data for many acceptable solutions, in contrast to inversion for a single, ''optimum'' solution. The GA is a directed search method which does not need linearization of the forward problem or a starting model, and it can be applied with a very large model-space. Consequently, fewer assumptions are required and a greater range of solutions is examined than with many other inversion methods. We apply the GA to fundamental Rayleigh group dispersion estimates for paths across Central Europe and across the East European Platform to determine ''average'', layered S velocity models separately for each region. The use of the GA allows an identical model parameterization and broad parameter search range to be used for both regions. The scatter of acceptable solutions shows velocity-depth trade-offs around the Moho, indicates the depth resolution of the inversion, and shows the uncertainty in upper mantle, S velocity estimates. The results indicate that a thicker crust and up to 0.3 km/sec (7%) higher S wave velocities in the upper 100 km of the mantle under the older East European Platform than under Central Europe explain most of the differences in the data sets. ¿ American Geophysical Union 1994