This paper presents the results of a study of the stress-strain state of a geodesic dome covering the planetarium designed in the city of Nizhny Novgorod. Four design schemes were created in the SCAD with different types of node modeling. A comparative analysis of the effect of the strain capacity of the “BrGTU” type unit on the stress-strain state of the dome cover has been carried out. The results are obtained on the change in the displacements of the structure nodes and internal forces in the dome bars, with rigid and hinged mates. The option of increasing the diameter of high-strength bolts to reduce the overall deformability of the system is considered. On the basis of the obtained results, it was concluded that it is necessary to take into account the strain capacity of the semirigid connections when designing mesh steel domes.