While rebuilding the famous "Church of Our Lady" in Dresden the authors have investigated the moisture behaviour of the sandstone cupola. The climate in the space between the outdoor an indoor shell has been simulated, starting from the climate in Dresden and the climate in the church as it depends on the ventilation and the frequency of the visitors. Then the moisture fields within the external and internal sandstone shells has been calculated by the computer code DELPHIN including the westside, which is the most exposed position concerning the driving rain. Periodically, during both winter and summer, water vapour condensation took place on the inner surfaces. The condensation effect can be reduced by a specially designed hygroscopic plaster. This and other measures of reducing the risk for moisture damages will be discussed in the paper.