Chimney stacks characterize many heritage buildings and often have high architectural and cultural value. Huge quantities emerging from rooflines are visible in almost all old town centers and monumental buildings. In many countries, the chimney stacks are the witnesses of the past and are protected as cultural heritage. Their variety is wide, with geometries and original vent caps that become typical and distinctive of specific neighborhoods or cities. The shape and geometry mainly depend on the architectural language of the building time, fireplaces' evolution, historical period and geographical area. Chimney stacks underwent heavy damage and failures, even under slight earthquakes, because they are typically the tallest component in buildings and experience large amplification of ground motion. Besides, they are often subjected to various degradation phenomena, with loss of structural integrity and load-bearing capacity. During an earthquake, most tend to break at the roofline level and fall either through the roof or outward onto adjacent buildings or public pavements. Therefore, in addition to the loss of cultural heritage, their failure can yield huge damage to the underlying building, and is hazardous to public safety. In this paper, a procedure to study overturning failure mechanisms is developed and presented. The behavior is studied through the linear and nonlinear kinematic approaches. The filtering effect due to the underneath building structure, which modifies the ground seismic input, is considered through floor response spectra, as advised by recent seismic codes. The procedure, applied to high chimney stacks of the Royal Palace of Carditello, built in 1787, is suitable for analyzing numerous historical masonry chimneys, to identify the most critical situations where it would be necessary to intervene in advance.