In geostatistics, spatial data will be analyzed that often come from irregularly distributed sampling locations. Interest is in modelling the data, i.e. estimating distributional parameters, and then to predict the phenomenon under study at unobserved sites within the corresponding sampling domain. The method of universal kriging for spatial prediction was introduced to cover the problem of spatial trend effects. This is done by incorporating linear trend models, e.g. polynomial functions of the spatial co-ordinates. However, universal kriging is sensitive to additive outliers. An outlier resistant method for spatial prediction is median polish kriging. Both methods have certain advantages but also some drawbacks. Here, universal kriging and median polish kriging will be combined to the robust spatial prediction method called modified median polish kriging. An example illustrates the method of modified median polish kriging along with piezometric-head data from the Wolfcamp–Aquifer. Copyright © 2001 John Wiley & Sons, Ltd.