The article is a brief review of the research of the stress-deformation state of a structure that represents a hemispherical geodetic dome exposed to the dead load. Single-contour geodetic domes composed of flat plates are the subject of the research. The process of their design has two stages: (a) design of geometric models of geodetic domes and (b) analysis of domes. The authors demonstrate that the first stage can be implemented through the employment of the library of ArchiCAD objects. Supplementary research is needed to have the second stage implemented. The objective of this research is to present the results of the research using computer-aided methods of modeling of metal structures. The analysis of smooth hemispherical domes is performed using analytical and finite-element methods within the Patran/Nastran environment. The authors demonstrate that the results of the finite-element method analysis converge with the results of the analytical method analysis. Conversion of geometric models of geodetic domes into the format that satisfies Patran preprocessor requires the employment of the Visual Basic software. Ultimately, comparison between the results obtained in respect of the geodetic dome and the analytical results obtained in respect of the smooth dome exposed to the dead load is performed. The conclusion is that the maximal stress experienced by a single-contour geodetic dome, in the event of reduction of sizes of plates, converges with the maximal stress of similar smooth domes.