Classical monuments, although made by stone or marble pieces placed one on top of the other without mortar, are stable against earthquakes. Their good seismic behaviour can be attributed to the sliding and rocking of the structural blocks during the strong ground shaking. Unfortunately, damages, which usually exist in such structures, significantly decrease this stability. Previous investigations on the dynamic response of classical columns showed that an initial inclination and/or corner cut-offs of drums may lead to collapse during a medium-size earthquake in spite of the fact that the structure has survived much stronger seismic events in the past. One type of damage, which is common in monuments, concerns fractures at the structural elements due to imperfections of the original material. During a strong earthquake, existing cracks open threatening the stability of the structure. In this paper, an investigation of the seismic response of monuments with fractured structural elements is presented. The distinct element method was used for the analysis and the model employed concerns a part of the Olympieion in Athens, Greece. The results show that the degree of the crack opening during an earthquake increases almost linearly with the peak velocity of the ground motion and the number of repetitions of the excitation. If significant shear and tensile strength exist at the crack interface, a stronger seismic excitation is required, in general, to cause failure. Cracks at column drums do not endanger the stability of the structure, unless they produce wedge-type pieces, which may slide during the earthquake.