Nowadays, more and more buildings are being constructed from various types of modern materials. Many works have been written about these materials, which primarily focus on the influence of their properties on the thermal and acoustic insulation of, for example, building walls. However, there are very few publications analyzing the influence of construction materials on the dynamic properties of building structures and their vibration behavior. Yet, vibrations are dangerous for building structures. In the analysis of dynamic issues, the dynamic properties of objects should primarily be taken into account because the dynamic response of a building depends on the values of these parameters. This article focuses on numerically determining and analyzing the impact of load-bearing wall construction material on building dynamic properties—natural vibration frequencies and mode shapes. Seven building construction materials were considered, and then nine variants of building load-bearing walls made from these materials were analyzed. The analyses were carried out on the example of a low-rise administrative building structure. The building was modeled using the finite element method (FEM) with three-dimensional (3D) model analysis. Three variants of 3D FEM models were proposed, validated, and compared. A notable impact of load-bearing wall material properties on the natural frequencies and mode shapes of building structures was found. Two issues could be mentioned as the main new contributions of this paper: numerical analysis and comparing the effect of various building construction materials on dynamic building properties and the proposition and validation of various approaches to 3D FEM building load-bearing wall modeling. The findings of this research are of important significance and should be taken into account when constructing buildings subjected to dynamic loading or analyzing the possible harmful effects of various types of vibrations on buildings.