Geochemical mapping requires a good understanding of geochemical variables and proper use of mathematical and mapping techniques. In this study, GIS mapping for the geochemical variables in Irish soils was achieved using trans-Gaussian kriging following investigation of probability features, outlier identification, optimal power transformation by the Box–Cox method and spatial structure modelling. Relatively high nugget effect values for the variogram models were observed for most variables. The assumption of spatial autocorrelation was seriously breached by two variables, available P and available K, and spatial interpolation was not performed for these. Two or even three nested theoretical models were needed to model variogram structures for most variables reflecting their variation at different spatial scales. The spatial distribution patterns for most elements illustrated the influences of underlying bedrock and soil type, while some of the heavy metals (e.g. Pb, Zn and Cu) were also affected by mining activities and urban sprawl. The available nutrients (P, K and Mg) appeared to be most affected by agricultural activities.