In structural construction practice, the use of reinforced concrete slabs is extremely common due to their structural and economic advantages. An important issue is the study of structural behavior given to horizontal effects. The significance of this is centered not only on the scales caused by wind and construction loads, which are considered to be “normal” i.e., the quasi-static, which is essentially one-way monotonically increasing but also the most researched seismic, i.e., cyclically varying, direction and magnitude effects. The most widespread methods for sizing flat plate slabs to unidirectional, quasi-static horizontal loads are the so-called Equivalent Frame Method and the Effective Beam Width Method. In addition to analytical and basically linear numerical theoretical methods, several laboratory experiments have been performed and published. In this paper, we investigate the behavior of column-supported flat plate slabs against unidirectional, monotonically increasing horizontal loads using an advanced nonlinear numerical modeling method. Numerical models constructed with different geometric dimensions were created with ATENA 3D three-dimensional nonlinear finite element software. In the numerical studies, in addition to the vertical loads in the global sense, the horizontal loads were also taken into account. In our studies, we analyzed the global behavior of the structure, crack propagation, and internal stresses. The results were illustrated on force - displacement diagrams and compared with the results of the laboratory experiments used, thus showing the accuracy and limitations of the numerical modeling procedure. The numerical results were also compared with the results determined on the basis of the equivalent framework models.