Principles of a new method of processing geochemical data on a computer, the method of multidimensional fields (MF), are considered. The method is based on interpreting geological space as the identification and construction of fields which differ from one another by different associations of chemical elements. The concept of natural geochemical associations is introduced. Multidimensional analysis is based on an automatic classification, separating associations of chemical elements according to values of their concentration coefficients (CC) and by taking into account their dispersion. Associations of elements are determined through factor analysis. By solving the problem on a computer, polyelement and monoelement maps are obtained, as well as their numerical description-namely, a table of concentration coefficients and mean values of proportions in each class (association), their dispersion, and other pertinent statistical data. Principles of interpretation and determination of the formation, to which geochemical fields belong, and of the zonality of association of elements are described. The MF method may be useful for geochemical surveys in any environment and various scales. It provides qualitatively new, useful information through use of the entire range of elements analyzed and of their interrelationship, as well as its representation as sequentially superseding associations in space (zonality of associations of elements). Case studies of different-scale geochemical fields are reported.