The design of a 69 m tall multipurpose building was investigated in this paper. The shape of the structure above the ground was an elliptical cylinder. Under the ground, the building was extended into a cuboid shape (for car parking). External wind pressure coefficients were determined using three methods: wind tunnel tests, CFD, and “the simplification of the shape” (using information defined in building standards). From the obtained results, it was evident that the simplification did not provide results with sufficient accuracy. The external wind pressure coefficients presented in this paper should be used for the design of a similar structure. The shape of the elliptical cylinder is very sensitive to applied wind. Positive pressures only occur on a small area of the windward side. The rest of the windward side is loaded with negative pressures. Therefore, torsional effects can occur, and these can be dangerous for the structure. The leeward side is completely loaded with negative pressures. In our case, this information was necessary for a follow-on static and dynamic analysis of the building. Various subsoil stiffness coefficients were considered. The calculated horizontal displacement was compared with the limit value. A measured wind direction of 20° caused the maximum obtained torsional moment, and a wind direction of 90° induced the maximum obtained force. The commercial program Ansys Fluent 2022 was used for the CFD simulation. The SCIA ENGINEER 21 program was used for follow-on analysis. This paper presents brief information on the selected turbulence model and details the settings used for the CFD simulation. Also, a description of the wind tunnel laboratory utilized in this study is provided, along with a description of the measuring devices used and the methodologies of the tests carried out. The main purpose of this paper is to show how important it is to consider the wind load for the static analysis of a structure like this.