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This paper includes main theses, proofs, and procedures of Boundary Element Method (BEM). The computer program. announced in 1981, for the calculation of stresses and strains around underground opening was used, comprising plane strain state for elastic continuum. Preprocessor with interactive input and postprocessor for graphic presentation of the results have been added to the program. In the main program the influences of various support systems for underground rooms were added, especially: shotcrete layers, steel arches and passive and prestressed bolts. This numerical method has been under current development, especially for materials with nonlinear behaviour The method is faster than other numerical methods and represents an efficient supplementation to them (the paper is published in Croatian).