Seismic assessment of structures is a challenging process due to the numerous uncertainties involved. Among the most significant uncertainties are seismic hazard, material properties, detailing, modeling complexity, and the type of analysis used. In the case of structures belonging to cultural heritage, the difficulty of seismic assessment is even greater, as these constructions were built hundreds of years ago based on empirical and intuitive criteria, reflecting the knowledge of their time. Additionally, these structures have endured several earthquakes, leading to accumulated degradations in terms of stiffness and strength, which cannot be quantified through an objective measurement. The article presents the seismic response evaluation using nonlinear and linear analysis methods, for post-byzantine domed churches, belonging to cultural heritage. The study focuses on the infirmary’s church of Cozia Monastery, dedicated to “Saints Peter and Paul,” listed as a historic monument in Romania at position 357, with the code VL-II-m-A-09697.05 [13], and dated 1542-1543. It is well-known that the presence of a dome distorts the structural response. Therefore, the article highlights the differences in structural response between the analysis methods commonly used in design practice (linear analysis) and the more complex analyses—nonlinear analyses. The primary source of uncertainty for vulnerability assessment of the church of Cozia Monastery infirmary is the seismic action. Given the variability of seismic action, the structural response must be expressed in probabilistic terms. Finally, fragility curves are computed.