Among the buildings with strategic role for civil protection purposes part of them were built before the introduction of modern seismic codes. Aiming to guarantee their operability in case of seismic events, they have to be assessed and, hopefully, seismically upgraded. This aspect arises the necessity of reliable low computational demanding numerical models and probabilistic strategies that can be easily adopted in case of the assessment of conspicuous building stock. Part of the authors proposed and validated, in previous works, a low-demanding seismic model calibrated on ambient vibrations (SMAV) that is engaged in this paper for calculating fragility curves. On the base of dynamic and geometric properties, the SMAV model simulates the dynamic response of buildings. The herein proposed procedure adopts the SMAV model and takes into account the direction of seismic input in a probabilistic manner. The use of the ASI scale as an Intensity Measure parameter is discussed and the results are compared to those obtained with others IM scales. Although SMAV implements an equivalent linear procedure the results are compared with those obtained by more sophisticated FEM models and nonlinear dynamic analyses with a satisfactory agreement. Finally, two real case studies are presented. The fragility curves for both the case studies are calculated and discussed. The results encourage the authors to the use of fragility curves based on SMAV model. Additionally, the fragility curves can be easily implemented in seismic risk assessment procedures at urban or territorial scale and, consequently, the proposed procedure may represent a key aspect in the reduction of seismic risk and rationalization of investments for the seismic upgrading of strategic buildings.