The paper presents the analysis of a pipe system using numerical methods. In order to be able to approach the analysis of a pipe system, it is necessary to know the theory of that particular norm and to know how to verify the results obtained by different methods. Pipeline analysis is mostly done with specialized software tools, but as such they must not be unknown to engineers. Engineers need to know how the software package works. The first chapter describes the problems or conditions that may occur in the pipeline systems as well as the ways of their failure as a consequence of these conditions. Further in the paper, stresses in pipelines that can occur under different load conditions are described. All types of stresses that can occur on thin and thick pipes are described in detail. Stress distributions through wall thickness is presented, as well as certain formulas from the Euronorm for the calculation of wall thickness. The paper further describes methodology of supporting the pipeline, methodology of calculating distance between the supports as well as the selection of proper type of supports and the calculation of the maximum allowable deflection of the pipeline – all requirements which are ordered from the investor. After that, the stress intensity factor and its application in the finite element method is explained and data is confirmed with the actual experiment for obtaining the stress intensity factor, as well as the computer methods for determining it. The calculation of the pipeline with different software packages is shown to point out the differences in results that can occur if different pipeline analysis software packages are used. It is explained how to interpret certain results for different finite elements. The complexity of pipeline calculations in the Ansys software package using a beam finite element is presented. The analysis of one high-pressure pipeline in the Rohr2 software package is presented including definition of all necessary parameters required for analysis. The analysis of the influence of the stiffness of the supports on the forces, displacements and natural frequencies for six cases of pipeline loading is presented as the final part of this thesis. The results are presented using diagrams and tables.