A typical subsurface environment is heterogeneous, consists of multiple materials (geologic facies), and is often insufficiently characterized 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 demonstrate that the Kernel Support Vector Machine is a viable and efficient tool for facies delineation, and contrast it with existing geostatistical approaches. To illustrate our approach, and to demonstrate its advantages, we construct a synthetic porous medium consisting of two heterogeneous materials and then estimate boundaries between these materials from a few selected data points. We also introduce and analyze the use of regression Support Vector Machines to estimate the parameter values between point where the parameter is sampled. Our analysis shows that the error in facies delineation by means of Support Vector Machines decreases logarithmically with increasing sampling density.