This technical study on strengthening a five-story building in Bucharest, a city known for its high seismic activity in Europe, required implementing a base-isolation system as part of the rehabilitation solution. The main challenge was assembling the elastomeric equipment system at the base of the building and the structural system, which was considered a rigid solid with six degrees of dynamic freedom. This required defining and solving differential equations of motion for earthquake action. It was determined that switching from a six-DoF system to a three-DoF system and then customizing the results for one DoF was justified. The analysis involved designing an isolation system with elastomeric anti-seismic devices and using a dynamic model with degrees of freedom to calculate the response for the first mode (fundamental) of seismic action from the spectral composition of an earthquake. The variation in amplitudes in the three zones—pre-resonance, at resonance and after resonance—is of great interest from a practical and design perspective. Also, the support solution was optimized in terms of the isolators’ location and the stiffness and damping parameters so that the degree of dynamic isolation could be achieved at the highest possible values (I ≥ 60%).