A typical subsurface environment is heterogeneous, consists of multiple materials (geologic facies), and is often insufficiently characterised by data. The ability to delineate geologic facies and to estimate their properties from sparse data is essential for modeling physical and biochemical processes occurring in the subsurface. We study the problem of facies delineation in geologic formations by means of a subset of the machine learning techniques - the Support Vector Machine (SVM) and its mathematical underpinning, the Statistical Learning Theory. To demonstrate the potential of the SVM, we randomly generate a two-dimensional porous medium composed of two heterogeneous materials, and then reconstruct boundaries between these materials from a few data points. We analyse the accuracy of the SVM facies delineation, and compare the SVM performance with that of a geostatistical approach.