The article presents the basic rules for constructing and training neural networks called the Support Vector Machine method as well as possible applications for this kind of network. SVM networks are mainly used for solving tasks of classifying linearly and non-linearly separable data and regression. However, in recent years more applications have been found for them. The networks also solve such problems as the recognition of signals and images as well as speech identification. In this paper, non-linear SVM networks have been used for classifying linearly separable and non-separable data with a view to formulating a model of displacements of points in a measurement-control network. The points of the measurement-control network were placed on a civil engineering object located on expansive soil (linearly separable data) and represented a mining exploitation area (linearly non-separable data). The task of training SVM networks requires the use of quadratic programming in search of an optimum point of the Lagrangian function in relation to the parameters being optimised. In the case of linearly non-separable data, the SVM method makes it possible to find a hyperplane which classifies objects as correctly as possible, and at the same time is located possibly far away from concentrations typical of each class.