This paper details how to construct a small-scale shaking table attached to a magnetorheological (MR) damper. The motivation for this construction relies on the increasing interest in modeling the dynamics of MR dampers—MR dampers have been used in structures for safety reasons. To model the MR damper, we use the so-called `Dahl model,’ which is useful to represent systems with a hysteresis. The Dahl model, validated through experimental data collected in a laboratory, was combined with a linear model to represent a two-story building. This two-story building model allows us to simulate the dynamics of that building when its floors are attached to MR dampers. By doing so, we can assess—through simulation—to what extent MR dampers can protect structures from vibrations. Using data from the `El Centro’ earthquake (1940), we can conclude that MR dampers have the potential to reduce the impact of earthquakes upon structures. This finding emphasizes the potential benefits of MR dampers for the safety of structures, which is a conclusion taken from the apparatus detailed in this paper.