The thesis briefly describes the characteristics of diagonal grid systems, and the advantages of using such systems. The calculation of two buildings was carried out, the first with a regular floor plan as an example and the second with a twisted diagrid system as the main topic of this thesis. Seismic calculation of both buildings was made using modal response spectrum analysis, and the behavior factors were taken from academic papers that researched such systems. Due to the irregular shape of the twisted diagonal grid system, it was necessary to study and apply calculation methods that are not fully covered and described in the guidelines of European standards, ensuring the reliability of the designed building. As an additional topic, the effect of wind, which is the dominant load on the considered building, was particularly investigated. The values of wind action according to the European standard and the values obtained from the computational fluid analysis, for which a specialized computer program was used, were compared. The application of the specialized program was calibrated by adjusting the simulation parameters for the construction of a building with a regular floor plan, comparing the results obtained with the results obtained according to the European standards. The obtained calibrated parameters were applied on analysis of the twisted diagrid system. Connections were calculated for the final designed model of the twisted system of the diagonal grid, plans and overview drawings and drawings of characteristic construction details were made.